If you want a game with awesome pieces, find a (complete) set of Hero Quest. That was another multi-week eBay hunt for me. But it rules and can be played with younger kids in a much more manageable time frame. I have no idea if there’s modern variants that capture the same feeling.
Another one you might want to check out: Legends of Andor. It’s a D&D-style fantasy board game, where up to four player co-operate to complete a series of quests. You’re still moving cool figures around on a map, and the co-operative nature means you can help the little ones with their turns without breaking the game. It also has an interesting mechanic where it feeds the rules to you gradually while you play, not unlike the first few levels of a real-time strategy computer game. It makes it easy to jump into, and presents a nice, gradual learning curve for the kiddies.
Also, it’s a lot of fun.
There were some other changes. Friends and I played… um, whatever version was out in the early-to-mid 90s, issued by “Supreme Commander Milton Bradley” 
back in high school. At some later date (in the 2000s), the most enthusiastic of us got one of the reboots. There was some change in the map–not just appearance, but how/which territories linked with each other. And there were other changes… but I have no idea what they were, at this point. However, aside from the substantive changes to the map, I agree that most were cosmetic. National advantages, maybe? I dunno.
(I remember the map changes because they allowed me, an atrocious A&A player at best, to actually win a game because the player playing Germany didn’t notice that two territories were connected. :D)
I’ve found the key to be UK building a IPC in India. Japan’s only defense is to also build one along the Asian coast, or they get gradually driven out.
After that, UK drops 3 tanks in India each turn, spends the rest on ships or planes back in England to harass Germany, trying to buy time for the USSR and USA.
Other recommendations: Flash Point and Pandemic. In Flash Point you’re firefighters trying to rescue the occupants of a burning house. In Pandemic you’re medical scientists trying to stop a global plague.
Both games are simple and easy for kids to learn and follow. Neither game is overwhelming in its need for strategic planning. Both games start out relatively slowly and the pressure builds as the game progresses (the fire and the plague spreads with every turn).
And here’s a main one: they’re co-operative games rather than competitive. All of the players are on the same side playing against the game itself. So adults and kids are not competing directly against each other. If one player has a run of bad luck or is less skilled, the other players can pick up the slack rather than push them to defeat.
If we’re talking the original game, they better take the infantry from Anglo-Egypt Sudan and Syria and transport them to India on turn 1 or Japan can take it on the second turn, if they do than Germany will have a much easy go of it in Africa. Russias busy, those few Chinese soldiers aren’t going to survive the first turn so a decent Japanese player with anything but piss poor luck should have your shinny new British factory by turn 2 after they’ve killed the 3 tanks defending it, net cost to the Brits 30 and you saved Japan 15.
Yeah, a UK factory in India is pretty vulnerable. It depends on how things play out, of course, but I’ve learned to be wary of it.
Descent is a cute game. I got bored with it after a few plays, mainly because I managed to build a perfectly optimized character at one point. After that the game felt lackluster, kind of like how it’s difficult to enjoy a computer game once you’ve played with cheat codes.
Well, additionally, the Russian player can contribute by flying fighters from Moscow and Karelia to India on his first turn. It’s a risk, to be certain, but the Japanese player would either have to build an IPC of his own (if he wants to be conservative) or all-out attack India on his first turn (if he wants to, y’know, go all banzai and shit), though this limits his ability to maintain initiative agasint the USA.
Or he can do both, I guess.
If Germany takes Karelia on its first turn, the UK can counter-attack… Basically, if the Allies coordinate, the odds improve significantly for them.
If you have older people and about eight hours get A&A: Europe and A&A: Pacific and make one giant board. You can have as many six people play at once. It’s a great game, but if you’re Japan DO NOT attack China, the UK, the USA, and ANZAC on the first round. I speak from experience. 
As for the differences between the basic game and later versions: they’ve
1.) added new pieces: motorized infantry, artillery, cruisers, destroyers, and tactical bombers
2.) Changed the technology rules (the Xeno 3.0 unauthorized version has the best tech rules IMO. The USA can develop nukes.)
3.) Added the concept of sea and air bases
4.) Changed the sequence of play. In most versions, I’ve seen Germany goes first.