I love how the Huns fill the same role they did IRL. They roam, conquer and pillage until other civilizations become powerful enough and start working together to wipe them out.
I've found the Hunnic AI very disappointing - Attila can't use rams because the AI still thinks they're a Spearman UU, so it will park them in good defensive positions or try to use them as a defence when you attack them. The Hunnic units are too different and along different tech paths for the AI to coordinate them effectively. Either he attacks too early, without archer support, or he techs late and battering rams are already obsolete because I'm already using swordsmen.
I've had two starts with Attila as my closest neighbour, and one where he was second-closest. The first time it genuinely worried me (and did cost me a minor city), but even taking and razing one city (which doesn't really benefit the Huns' strategy in any way) cost Attila his army and he was on the defensive and hemmed in his capital for the rest of the game. He also seemed reluctant to declare early war despite provocation (I'd been asked to denounce him by a CS, and while it didn't seem a smart career move I did it anyway. He just sat there seething). In the second he rushed Bronze Working for his rams, and then attacked - good call, except that of course he had no ranged support (Attila seems never to build ranged units until he has his Horse Archers). Battering Rams struggle in rough terrain due to their low movement and defence, so most cities will be able to fend them off without being hit.
When he was my second-closest neighbour he seemed to do moderately well, but made the mistake of declaring war on me before he'd finished off Mongolia. Genghis had lost a city and there were Hunnic forces closing on Karakorum, but by the time I arrived he hadn't managed to actually attack the city itself and once I'd helped clear his forces the Mongols had a clear path to his city (fortunately for Attila they accepted a peace offer, although they only survived until the end of the game because I decided to let them keep their final city, having finally taken Attila's Court in a subsequent war. In a late resurgence of hostilities Genghis was closing in on that city when the game ended to a German space race victory).
EDIT: These games were on Emperor as well. A couple each of archers and warriors tends to finish Attila's early rush, and then he's spent, quick knights notwithstanding.
the restart civ for me is Germany if they are close enough to make trouble later on but too far away to take out early.
Haven't played for a few days, but at my current game stage (T90 or so) the Germans are indeed close enough to make trouble, have made good progress (with their now-enemies Siam) in defeating Sweden, and just denounced me. I responded by signing defensive pacts with Siam (with whom I think the Germans are currently at war) and the Iroquois, so it will be interesting to see how this plays out.
I find him highly entertaining and he usually shakes things up.
Against my better judgment - since he's not performed well as a warmonger and in my latest game I found his incompetence in our war the one time I've really been annoyed by how weak Civ V's combat AI can be - so do I, just because it's now routine for me to find him in my games (okay, only three times, but I haven't played many G&K games yet) and he's been an aggressor every time which has given me a lot of stories about the time when Attila did this or that...
And yes, he's a great schoolyard bully character. I love getting notifications that he's bullying all my CSes, and even if his military underperformed his gunboat (well, battering ram) diplomacy in my latest game was fantastic - he moved a bunch of rams right outside my territory, and then contacted me to say "I'm awfully sorry, I just bullied one of your city states. Will you forgive me?" with a very clear implication what would happen if I said no... I actually do think Attila is one of the "truer to life" Civ V characters - yes he's best-known for going on the rampage, but in reality he could be bought off (and was) diplomatically for a time or redirected against other targets.
There's also something immensely appropriate about his warnings that your army's a little on the weak side and he's surprised you haven't succumbed to a barbarian invasion.