The big difference between Dominion and Ascension was, as has been pointed out, a difference of complexity.
Ascension basically boiled down to 'capture ALL the things!'.
Dominion has minion wave management, the question of who should grab the storm shield and when, bottom lane to control/gank, points to defend and take, zones of the jungle to control, and so on and so forth.
I suspect part of the reason why some people liked Ascension more was because it was simpler. It was really clear what you were supposed to do and the optimal strategies were obvious for the most part. Dominion has a lot of anti-intuitive aspects that sabotage new player experience. Probably the best thing Riot could do for the map on the low-effort side of things would be to either make pushing a minion wave a slightly more rewarding choice (or at least less of a trap option) and/or add some more objectives to the Jungle that would encourage proper control.