First off, godbless Sunhi for those gifs.
Secondly, the game is stunning, and it shits on TR13 visually and presentation wise. But those gifs don't really sell the combat well. I played on hard and if you dangled on the rope that long you are fucked. It's cool but it lacks the variety of TRs combat. The AI allys constantly moving around and not getting caught just takes me out of UCs combat at times.
For all the heavy attention to detail praise UC gets, it's really jarring to see your the NPCs not do shit and brush off an enemy and not get detected. It's also worth noting that before UC4 the stealth in UC was terrible. I need to go back and play TR13 because it's been a while, but I think it'll hold up better than UCs combat overall. Holy shit at UC4s melee combat, best contextual melee system ever. I barely ever saw the same things twice.
I have to disagree on that one, I used the rope plenty on my hard playtrough. Timing is crucial but hard for sure allows you to make some well timed "reckless moves". And if you want to do that all the time because you think it is more fun, why not pick easy mode? There is nothing wrong with it and it can still be a challenge when you take the run n' gun playstyle.
As for the variety in combat, I really don't see how TR013 offers more variety. UC4 manages to blend different playstyles seemlessly. And in every UC after the first one, many shootouts are heavily influenced by the environment they take place in (especially UC3 excels at this), not just in terms of level design.