From what I've heard from a number of posts/people/a few websites: The AiME versions of the Warrior(Fighter), Slayer(Barbarian), and Treasure Hunter(Rogue) are pretty much (more or less) exactly the same as their respective 5E versions. The Barbarian gets a subclass that gives it Heavy Armor usage that doesn't interfere with Raging so it pretty much makes it harder to kill than the regular 5E Barbarian. The Weapon Master subclass of the Warrior has an amazing ability where it gets its own Weapon that is capable of scaling in a way and gaining a number of bonuses. Plus it has the unique feature of "Upgrading" a very basic selection of Fighting Styles. Which is a neat system in a way.
The Wanderer(Ranger) is functional ala the prior 3 but I think it's been said it loses some of it's useful capacity if your not porting over AiME's Journey mechanics over to your regular 5E games. The Warden, from what has been said, is basically a Spell less Bard. It's a little bit better with the Errata documents that come with the Eaves of Mirkwood starter adventure/DM Screen combo kit. This just gives the Warden's Herald subclass proficiency in Medium armor and Martial weapons IIRC as well as a few changes/substitutes to a few of its abilities.
Things become a bit more complicated with the Sage class and it may not work as well in regular 5E games. I say that all the prior classes mentioned will work without any major hiccups except for the Sage. This is mostly/probably due to the result that AiME is low magic compared to your typical DND games that aren't low magic as well or gritty. It too gets a number of useful errata in the Eaves of Mirkwood errata documents as well. As to whether it fixes its non-LoTR probs, I have no idea.
I for one say/encourage that almost all AiME classes will fit right in with non-LoTR games. Sage is probably better to add it's features onto an NPC though.