You just got lucky is all, no two barrels are alike... well unless they're from the same manufacturer.
Personally I'd use the original lid from the barrel. It's made to fit, and like others said with the Weber lid you'll likely have grease and smoke splooge dripping down the outside of your drum. You won't get that with the lid because the lip fits the inside. If you're concerned about less headroom with the flat lid rest assured, if you put your rack 7-8" down you'll be able to fit a turkey in there laying flat.
There is also debate about different cooking characteristics, dome vs. flat lid, but that's a whole 'nuther thread. Mine cooks AWESOME with a flat lid and short chimney pipe.
Good luck either way. UDS's are the best!
UDS, Akorn, Weber Red Head Kettle, Drum Grill, Gasser w/cobwebs all over it. I'm JD.