I've been playing TF2 since beta, both competitively and in pubs. Here are my thoughts on the matter. Be warned, there are a lot of them (this is about 3.7k hours worth of thought in one go):
The game peaked in terms of balance around the time of the first Pyro update. Pyro was pretty useless unless he had a pocket medic healing/ubering him, and the original airblast added some much needed utility. The first medic update was necessary in order to encourage people to play the class more, and also introduced Goldrush/Payload map types to the world which in many ways saved the game by focusing the action at a specific spot on the map and establishing a 'front' for both teams to bump into each other. Things became less chaotic and more organised and players found it easier to settle into a role than they had on tc_hydro or cp_well where things were less focused.
Things have gone downhill since then, with a slight improvement in the last 6 months or so. This is largely due to a practice of balancing the game based on the lowest common denominator, with consistent buffs to the lower skill cap classes (engy, pyro, heavy) to bring them into line with the higher skill cap ones (demo, scout, soldier, sniper). These buffs have not had the desired effect, as a good scout/soldier/demo player will still shit on a good engy/pyro/heavy player from a great height, but the latter classes are now infinitely more frustrating to play against. The key point here is that they're not harder to play against, they're just more obnoxious. As well as those classes, the same thinking can be applied to pretty much every unlockable weapon/item in the game.
As an example: The community servers I learned the game on had 4-5 really good Spy players who could be incredibly effective despite the weaknesses of the class. Good revolver aim, a lot of cunning and great map knowledge were their tools to consistently top score on pub maps. Then came buff after buff to Spy. Getting cloak from ammo packs reduced the need to sneak around or time your approaches to get behind the enemy team. It also made it incredibly easy to walk from one end of the map to the other completely invisible and spend the entire game sapping the enemy team's teleporter entrances. For a good year or more playing engineer became an exercise in frustration because you simply weren't allowed to have a teleporter up. The introduction of the Dead Ringer only made things worse, as teams were forced to play whack-a-mole chasing spies around and killing them multiple times. Anyone else remember shooting a spy and then immediately sprinting to the nearest ammo packs to deny them to him? Utterly obnoxious. A lot of the thought and art had been taken out of playing Spy to appeal to the 14-15 year old crowd who loved going for ambassador headshots without worrying about the objective or helping their team gain control of the map.
These suddenly obnoxious spies left a lot of Engineer/Heavy players feeling short changed, so of course they were the next two classes to get a buff. The buffs to Heavy to make him more effective at mid ranges (tighter spread) and more responsive (faster spin speed) led to the rise of an awful new presence in on payload maps: the Cart Heavy. Thanks to the free mobile dispenser the cart provides, Heavy players on offense can now go through an entire round without taking their finger off the shoot button and still be effective. It's made the game incredibly stacked in the favour of offense, and the standard has now become an absolute steamroll for the blue team until the final cap (which often have sentry gun placements that Heavy cannot deal with easily). Between this and the introduction of the level 3 teleporter, most maps are now played out pretty much entirely at the final cap point, where the red team sits in one place for 10 minutes and the blue team throws themselves into a meat grinder. There is a reason people talk about players going 'rage Heavy' when they're losing on offence.
The reasons for that meat grinder being so toxic/impossible to deal with are twofold. One is the buffs to Engineer. The introduction of the level 3 dispenser means that you can no longer trouble an engineer with longrange spam from rockets or pipes. Any damage you do to him is healed almost instantly, and you can no longer win a war of attrition by making him run out of metal. The introduction of the rescue ranger/wrangler also makes sentries far tougher to take out via positioning or ubercharge. Whereas there used to be a relationship between the Engineer and his teammates where the engy relied on his allies to stop the enemy team getting into a position to shoot his sentry gun safely, that is no longer a consideration. As a result, you'll often see 3-4 engineers and 3-4 snipers defending a last cap pretty effectively, whereas in the past this sort of immobile composition would have been crushed. On offense, the introduction of the level 3 teleporter has removed basically all consequences for death and encouraged people to play worse, getting in stupid positions rather than playing in a considered manner and trying to control parts of the map. Instead of being out of the action for ~20-30 seconds if you die, you're now only out for ~7 seconds.
Additionally, the standard of Medic play has reduced drastically, and the class is considerably weaker and as a result underplayed. The first reason for this is an indirect one. A few years ago, players started getting points for damage done as well as frags. This is a good change (since damage is more important than frags in TF2) but one thing it's done is made it very difficult to topscore as a Medic in a pub, when Medic used to get topscore every round pretty much by design as a way to encourage people to play the class. If you wanted to feel good about your score and win the adoration of your team, you went Medic. Additionally, because of the massive buffs to the Pyro airblast cooldown ubercharges are nowhere near as effective as they used to be, so one of the key elements of the class is now crippled. The other reason is that all of the alternate medibeams suck, but people persist in using them because they're seen as more fun. Hitting a really good Kritzkreig, microing the Vaccinator, or zooming around with the Quick-Fix is great fun, but all of those things are objectively worse at pushing through choke points than being invincible for 8 seconds, and the game is about pushing through chokepoints. In competitive play the Quick-Fix is so overpowered it's banned in every league, but in pub play when any enemy can randomly crit and instagib you it's pretty useless. This just means that the general standard of play is lower, more chaotic, and less of the structured/balanced game I used to enjoy.
The buffs to Pyro are also a big culprit for reducing the standard of play. The airblast was a great idea originally, giving the Pyro a self defense mechanism against long range projectile spam. Unfortunately in an effort to raise the skill cap of the hero they decided to make the class more about combination attacks and knocking players about the map. Firstly, getting airblasted is about the most frustrating experience in the world. It's nigh-undodgeable, and basically allows the Pyro to cast a stun/snare like he was a MOBA character. This has led to the airblast being the Pyro's main form of offense, rather than his flamethrower. Most players now will, on reflex, touch you with the flames to ignite you and then immediately airblast you so you can't move. This hasn't raised the skill cap of the class, it's just allowed players to shoot at stationary targets because they struggle to hit moving ones. The increased effectiveness also allows you to completely shut down an Ubercharge without requiring a great deal of skill or thought (as opposed to a Soldier knocking an ubered target around with well placed rocket), leading to far more durable defensive positions and more of that 'meat grinder' effect.
These are, in my opinion, the major reasons the game isn't as good as it used to be. It's a different experience now with more focus on solo play and random deathmatching, and less on teamwork/strategy. I basically steered clear of discussing too many of the unlocks because as a pretty good player (I've played at the top level in Australia) I see most of the unlocks as my opposition gimping themselves. The issue with the unlocks is that they're largely weaker than the stock weapons while at the same time being more annoying to fight against. This just leads to worse play and increased frustration. Before someone calls me out for being some sort of competitive elitist, know that my first two loves in this game were Pyro and Engineer, and that to this day I still think only 1% of the playerbase plays those classes to their potential (they were fine before the buffs/unlocks if you could aim your shotgun and work with your team).
That being said, the shooting/movement mechanics of the game are still great and I'll still keep playing it as my go-to shooter. I tried Overwatch but gave it up after less than a week because all 21 characters felt completely one dimensional. I just wish Valve had realised what a lucrative market E-sports was back in 2008, rather than dumbing the game down chasing the mass market. My dream is for TF3 to be released with competitive support similar to Dota2/CS: GO, but that's about as likely as the release of HL3.