Now, I never said budget wasn't important, just that it can be blown out of proportion. Allocation of budget does obviously occur, Space Dandy's trial episode for instance is an example of that, so that they could blow money on the finale. However, when there is good looking scene, some people tend to sometimes scream budget like some kind of soulless quantifier that automatically makes things look better when it's usually evidenced some notable key animator was responsible or a good storyboarder. Not the best example but most of Fate/Zero or Fate/Stay Night's best looking animation is arguably by Nozomu Abe, who is quite talented and not because he was given a lot of money.
Most production woes and ugliness are due to rushed schedules or perhaps bad management, so while obviously you need money to not have a ton of stills, it's usually not the biggest problem for studios especially when we know staff get paid peanuts for work. If a key animator and animation director list for an episode is relatively small, that's usually a good sign because they didn't hire tons of people to help meet the dead line, this is the case of a lot of KyoAni shows in general which have excellent scheduling while the opposite of that would be the infamous Attack on Titan. A-1 Pictures for instance is a studio that have bad schedules from time to time that catch up to them, see things like Magi S1 (Our in-between frames from China were late!), Nanatsu no Taizai, Kaito Kid etc. Even when they do manage to hold it together like Your Lie in April look at this comparison with Sound! Euphonium in the
number of animators for a performance episode.
There is also the consideration of Blu-ray corrections, if they didn't have enough money in the first place, why would they bother correcting things? See Wizard Barristers for a particularly nasty one.
In the case of your examples. SS: Omega, I imagine it is also due to being Toei-d, their workforce and talent are stretched really thin as they have ton of shows on their plate. A recent Toei business report states that revenue went up when they increased the number of shows being produced, so that says something about their production ethic I think.
It's true Denno Coil has the benefit of large budget but it also had gobs of serious talent that Iso recruited for the show probably with the help of personal connections and for being a renown animator. It also took a long time for Iso to create/plan the show for what it's worth.
