I've stumbled upon this older question about
Karma Points vs Numeric Levels
The answer there is claiming that a points system is better, one of the main reasons being
Points naturally give rise to levels, but points are more precise. Here, on StackExchange, we use points, but we also have implicit levels -- just look at your privileges tab. When I look at users, I usually group them into "levels" according to their rep (e.g. I think of 100-500 rep as being one of these levels).
Which is essentially true and seems to work well here on all SE sites.
What makes me think is that a few years ago the design team of Leaue of Legends (an online multiplayer game) changed their similar system to the opposite. Before, they the Elo System (adapted from the chess version), which was basically a skill represented by number, which is also what we have here on SE. So players compared themselves by point ranges.
Then they changed it to a "League System", where players collected points inside a league and could then move up to a higher one. I remember reading an article about how this system would make it easier for players to stay motivated, since it gave them smaller scale victories to hold on to (can't find it now unfortunately).
Both systems are essentially the same, but the expression and visualization of them vary.
On the other hand, another good argument for continuous points of the linked answer above was
How would you assign levels? How would you decide what merits level 1,2,3,...,99? You don't really know how this will play out. The great thing about points is that they're a simple numerical scale, which the users will gradually group into their own "levels".
Unfortunately that answer does not cite any sources.
So both examples, SE and LoL, provide some form of proof for their system but there's no actual comparison or a pros / cons listing for both, as far as I can see.
Which one motivates the user more to keep using the system?