Classic can be very nice in the sense that it rewards you handsomely for hunting enemies several levels higher than you. The areas with these high-level mobs are not always areas with high-XP oddities or lots of oddities, so if you want that exact gameplay experience, Classic is a good choice.
With that said, I love the more chill environment of Oddity where as long as I'm progressing in the game, I'm getting decent XP, period. All new areas have some new oddities, so as long as you're visiting new areas (and why wouldn't you, exploring the world is one of the most fun parts of the game) you won't be massively behind in levels, even if you're missing lockpicking/hacking/pickpocket/killing/quest XP.
Doing the things I want to do in the game is its own reward, I don't need to get XP for every thing I do. Even on Oddity you can have buckets of fun hunting higher-level enemies for the challenge. You might not always get a direct XP reward for it, but you're not massively penalized for any specific approach to the game either. If it's a new area, there's oddities there no matter how you want to clear it.
On Classic, there might be times when you don't want to kill anything, and you don't necessarily want to complete every quest. Quests and killing make up such a huge amount of the XP on Classic that you are pressured into doing things the violent way, and you develop a near-obsession with being a yes-man for anything that's asked of you (incidentally this player-behavior was satirized in Nier where sidequests were frequently tedious and lead to horrible results in-world with little material reward, with your companions straight up questioning why in the world you would do anything and everything someone asks you to, no matter how dubious).
As it stands, the way this new-area XP is expressed is that you do have to hunt through trashcans and the like. Perhaps not the best way of doing it, but I can't really think up of a better alternative either. Giving you automatic, instant XP for finding new areas wouldn't feel right, you should have to actually explore the areas. Walking to and clicking on objects in said areas is a reasonable way of doing it. Hell, it's the best XP system I've seen so far.