Ginaman, yes the Huns are powerful early on. But once you hit medieval era, you will find their power wanes.
Not a fair comparison, since it's an AI and the AI is uniquely badly-suited to playing the Huns (Battering Ram = unique spearman, puppet cities all game long), but Attila's doing better than I've yet seen him in my new Emperor game. I rolled a four-civ map - apparently two continents, one with three civs, the other with the remaining as-yet-uncontacted civ.
Attila actually behaved in a way I haven't seen from the AI before. His rush was late, and light on rams (though he turned out to have enough), but with a lot of Warriors supporting his horse archers; the AI even used them appropriately to do the fighting instead of trying to attack with rams. I was keeping my scout watching him, and prepared as he moved in my direction (as usual he was behind in tech, but this is a Hun thing more than an AI thing - no Pottery rush, no Libraries). He declared war on Kuala Lumpur, the perpetual punching-bag CS of my games and my close neighbour and protectorate. I moved my army too slowly - KL would have fallen the next turn. But Attila suddenly declared peace, perhaps an AI calculation that it was now in two wars (I declared on him as soon as he hit KL), and withdrew, basically blunting the rush.
Until he came back, to find Elizabeth still unprepared. So he took London - it's a shame that in a mutual war you can't get open borders without Civil Service (I was several turns away from it at this point). It didn't take long for me to take it back and, because I'm a sucker for being the good guy, I liberated Elizabeth (plus I was thinking of a diplo victory, although I'm currently both tech and culture leader. Starting CSes make a
big difference with Siam - I had two cultural and one maritime within reach from close to the start). Nevertheless, the Huns had adapted remarkably well - conserving most of their army after aborting the attack on KL, they'd actually expanded naturally several times. They're currently putting up a strong fight; capturing the (Hunnic-founded) city of Coventry took a while, and they then showed up with a giant army that forced me to retreat and leave the city to them (EDIT: Well, what I'm actually going to do is give it to Elizabeth - who isn't at war with them - which will at least remove the Hun army from the city's borders). Though this is now a standard game, the Huns have retired both their UUs (early Renaissance for them, two turns away from the Industrial Era for me).
Overall, though, aside from his rather pointless refusal to declare peace (gigantic army and all that) when I'd happily do so having achieved my main objectives, the AI is actually playing the Huns the way a player would play them - going for easy early kills, avoiding confrontations that will cost them vital units or time delays for the rush, and taking time out to expand and develop. It's working well - he's recovered somewhat from the loss of London, he's still behind techwise, but chances are so would a human player be.
And the AI's experience has lessons for the human - the assumption has been (and I'm equally guilty of it) that the Huns go in, grab a few choice early cities, burn out but still have a decent base to develop from. But bear in mind my earlier point that the Huns suck on defence in the early game (and even more so when they're carrying on the rush to hit the next target) - they get the big cities early, but quite aside from the challenge of the mid-game transition, there's no guarantee they'll hold on to the early conquests long enough to develop them into useful cities.
Overall I find the Huns very well-balanced - they're nowhere close to as strong as they appear on paper or on low difficulty levels, and indeed the challenge of using them well is such that in the hands of an average player they're probably a weaker than average civ, but the considerations you have to juggle as Attila - how to develop past the early game, how to survive the early game with your new conquests intact, how to mitigate the later-game effects of all those early warmonger penalties - make them a very strategic civ to play, and very much not a one-trick pony. Sure they have essentially one trick at the very start of the game, but then that's also true of, say, Babylon or the Maya, who follow stereotyped routes to early teching if they want to maximise their advantages.