MAGIC USERS: This class is dealt with here in only the most general terms: most of the magic user's special abilities come from spells, and his other abilities are further dealt with in the Dungeon Masters Guide. Intelligence remains their prime requisite, and they are still forbidden from using armor. Their range of weapons available has widened though: whEreas before they could only use daggers, now they are able to use staffs and darts.
Spellbooks are discussed briefly, and it's interesting to note the following: "as the magic-user advances in levels of ability, a book of spells for each higher level of spells which become usable will have to have been prepared through study and research." This says to me that magic-users need a new spellbook for every spell level, which I thought was new, but it's right there in OD&D. Silly me. This puts a pretty big crimp on spell-casters travelling on long journeys - you can't really fit nine spellbooks into a backpack. Re-memorisation could get difficult.
The enchantment of items and scrolls is glossed over, but no hard details are given. I guess they're in the DMG. As in OD&D, they have to be 11th level to start doing this.
Magic-users now have the option to build strongholds and tax the land, which I'm pretty sure wasn't an explicit option for them in OD&D.
The titles for levels 1 and 2 have been changed. In OD&D, they were Mediums and Seers respectively; now they are Prestidigitators and Evokers. There are also some new titles near the top of the chart: 16th-level magic-users are called Mages, and 18-level are called Arch-Mages.
A comparison of the XP needed to advance in level shows that, starting at 5th level, AD&D magic-users take longer to advance than those in OD&D. The gaps starts small, but grows wider with every level. The number of spells a magic-user can cast per day is comparable in both editions, with OD&D slightly edging ahead now and then before drawing level again. It's not until level 17 that OD&D pulls ahead in this regard; AD&D magic-users only win out because their chart goes all the way to level 29, while the OD&D chart stops at 22. OD&D wizards still get more lower-level spells.
ILLUSIONISTS: This class first appeared in The Strategic Review #4, and they are included here as a sub-class of magic-users. It's a little bit harder to qualify for this class now: in OD&D, a high intelligence was recommended, and a Dexterity of 15+ was necessary; in AD&D, Int 15+ and Dex 16+ are both needed, and having a high score doesn't grant them an XP bonus.
The major difference between magic-users and illusionists is their choice of spells. M-Us are probably more versatile, while illusionists have some powerful low-level spells, and can be used very effectively by players who can exercise them creatively.
The major weakness of illusionists is that they are restricted in the magic items they can use. As in OD&D, they can only use scrolls with illusionist spells on them. They can use all potions, except those restricted to fighters (in OD&D potions weren't mentioned as allowable items). They can no longer use Crystal Balls, but they are now able to use all rings (again, rings weren't mentioned before). They can also use the rod of cancellation, staff of striking, and wands of enemy detection, fear, illusion, magic detection, metal & mineral detection, secret door & trap detection, and the awesome wand of wonder. (This is a wider selection than they had in OD&D, but the wand of paralyzation has dropped off the list.)
The level titles for Illusionists remain the same, except that Prestidigitator has been inserted at level 1, causing all the others to bump up a slot. In OD&D they stopped rolling hit dice at level 11, but now they stop at level 10.
AD&D illusionists seem to get their high level spells quicker, while OD&D illusionists can memorise more low-level spells. AD&D illusionists need far less XP to advance (though it evens out around level 14).