Oddity system is a much better one because it forces a more comfortable playstyle unto the player. Or, rather, it's the common experience one that drives you into specific behavior. See, it's all about the experience scaling - specifically, different kinds of experience scaling differently. Monster experience scales down (the higher you are in level, the less xp you receive), quest xp is constant, skill xp scales up. Therefore, it's much more beneficial for you to rush into combat first, killing as many foes asap there, and leave the quest stuff for the later. As an example to this, one of the ways to powerplay Underrail's early game was, instead of gaining that introductory level at the station, to rush straight into the caverns, slaughtering rathounds for that sweet 90 xp per body gain. And then you followed it through to that compound area, killing rats until you were almost level 3 (that's when they ended). If you did stuff this way then, at the end of introductory mission, you would be almost level 4. If not 4 already. Huge difference.
And so forth, and so forth. Of course, maybe I'm just a compulsive metagamer, but at the same time it always felt like the system was punishing you for not rushing into combat. Though, at the other hand, it also punished you for fighting the monsters too early - after all, there was a penalty for overleveling the monster but no reward for fighting it too early. So it also created this "Am I doing this right, am I not screwing myself here?" feeling. And let's not forget that combat can be pretty brutal in this game so screwing yourself is certainly not what you want.
Also, that system created lots of backtracking - oh, no, why would I finish this quest now when I could do it 5 levels later when the experience will be more precious than now? Oh, no, I won't open this cluster of 4 locks, I'll wait for some more so I'll gain an extra hundred xp out of this. Once again, you can blame personal habits here, but the game is hard enough to compel you into stuff like this. Whereas with oddities this is just cut off. More than that, you don't even feel the need to do some stupid stuff. Like, why would I bother to disarm these stupid mines when it's faster to blast them away? Or why would I open to pick that lock if it opens a route that I've already explored from the other side?
And one additional boon of the oddity system is that it creates different tempo for different characters (which isn't that strongly present in the average version). For example, upon arriving into a junkyard, a thief can steal both gangs' oddities, earning what, 6 points in the process? That's almost a level. Whereas the other classes will probably also gain those oddities, but not until much later into the game. It's a help to the stealth characters and, considering how much effort was put into creating a decent stealth system in this game, that's certainly appreciated.
