I've always gone Oddity since I believe that's the "intended" way to play, but people tend to fall back to classic after many playthroughs, since it lets you skip content you don't want to do without penalizing your ability to reach max level.
If you intend on clearing most content, Oddity is fine. Note that I always play with Lockpicking/Hacking/Pickpocket myself, and Oddity is very rewarding for that playstyle (especially Pickpocket), while builds without thieving skills tend to level up slower. Without pickpocket, you often have to end up killing innocent NPCs to get their oddities, which might not be your thing.
Overall, I find Oddity to be one of the more interesting unique features of Underrail. It's been so fun to infiltrate well-guarded outposts freely (ie: without having a quest to do so) and be rewarded with unique oddities. It's just too bad non-DEX builds have to sacrifice so many skill points, I wish there were more STR/AGI/PER checks to get oddity duplicates for those other playstyles