I feel HGSS had the best "out of menu" botton screen UI, but the worst bag UI. Clicking menus directly is awesome and all, but having to browse through 6-itens pages in the bag is incredibly clunky. You take ages to find anything, and the lack of an auto-organize feature just makes it worse.
My main gripe with current UI is the box system, and the lack of options when dealing with batches of pokemon. First, there is no option to release more than one pokemon at a time. In a game that incorporates chain breeding, in which you have to possibly go through HUNDREDS of eggs before hatching something with perfect stats (assuming you aren't using Hacket or RNGed dittos, since that's not intended), having no way to quickly get rid of all the leftovers is horrible. And Arceus help you if you ever dabble into MM'ing eggs for competitive shinies. You will have to literally release THOUSANDS of lv1 leftovers.
There also should be an option to deposit, in any order, a bunch of pokemon into a box. Right now, you have to browse through the boxes, one at a time, and then manually put the group of pokemon there, only if the pokemon are arranged in a way that fits perfectly the empty space in the box. HGSS had a box feature that allowed you to move a pokemon to another box, in the first slot avaliable, without changing your current box. Being able to do that for whole groups would be HUGE. Even better: allow me to select a row of 5 pokemon and throw it at my curret party/battle box. Or allow me to make whole batches of pokemon switch places with one another. Why isn't that a thing?
By the way, does anyone use that blue selection mode thingie? What's that for?