How does this work in Morroblivion? Are the skills and attributes requirements still there or are they changed around somehow? I'm afraid I don't even know the differences between Morrowind's and Oblivion's systems. And I'm sure this is out there somewhere, but couldn't find it with a quick search.

Only the major skills are
Only the major skills are required for faction advancement. The minor skills were just too much to keep track of.
For example:
In Morrowind to get to Lawman in House Hlaalu, you needed Speed 30, Agility 30, and one favored skill at 30 and two favored skills at 5.
( The favored attributes for House Hlaalu are Speed and Agility. The favored skills for House Hlaalu are Light Armor, Marksman, Mercantile, Short Blade, Security, Speechcraft. )
In Morroblivion, to get to Lawman, you would just need Speed 30, Agility 30, and one favored skill at 30. The 'lesser' requirements (2 skills at 5) are removed for all of the different faction ranks in all of the factions.