The leveling system from from oblivion was reworked:
1. In base oblivion only major skills contribute to your player level. In the remaster, all skills increase player level. You're potentially leveling up three times as fast as base oblivion.
2. In base oblivion the skills leveled affect how many attribute points you get, anywhere from 3 points to 15. In the remaster you get 12 points to distribute freely no matter what.
3. In base oblivion attribute bonuses are dependent on the level at which they occur; leveling endurance early is super important. In the remaster they are applied retroactively.
This was done because base oblivion suffers from something called "the leveling problem"
A player level is triggered once you raise any of your major skills a total of ten times. But it's not possible to get the maximum number of attribute points by only raising major skills. If a player wants to take full advantage of the system, they must put 2/3 of the skills they actually use outside of their major skills in their minor skill category, and level major skills 10 times per level and minor skills 20 times per level. If you micromanage each level-up and futz around with this system you will get 15 attribute points per level. If you only use major skills you will gain about 6 attribute points. If you only ever use skills from the major skill category, ie. the skills from your class, your character will become worse overtime relative to the enemies you fight. As a result most people either stay at level one the entire game, install a mod to fix it, or wonder why the game is getting so hard out of nowhere and drop the difficulty to easiest.
Overall I think the remaster has a good middle ground, but It's obvious why they axed attributes for Skyrim. It is anything but intuitive.