For me, the perfect burger means that all the individual components are on point.
Starting with the bread. It must NOT be cold/soggy. Traditional sesame buns are ok, but brioche are superior. Everything inside must be fresh too. The meat is also really important obviously.
Another crucial part is that it must be balanced. I don't want it to be 90% meat. And neither do I want the burger to be half a foot high, that way I can't actually eat it all at once. There is not point just eating one part of the burger at one time. I might as well have it separated out on a plate in front of me.
Anyway, had an Honest Burger last week at the new-ish joint they have opened up here in Tooting, London. It was really good. The brioche bun was nice, salad inside was fresh, and the meat was really well done. It was medium rare, but not just reconstituted mush... proper meat in there.
Had Five Guys twice now in London, and found it slightly disappointing compared to other burgers I had in the states. Put together very rushed and worst of all.. the bun was not reheated properly!