This spring I took on the exercise of modifying my wife's triathlon bike which she no longer intends to use into a TT-legal bike (they actually check here so you've got to conform to the UCI rulebook - saddle setback and distance from the BB to the handlebars ends and all that), with about zero previous experience riding in aerobars. Anyway, after making it fit acceptably well on the trainer, I took it on the road to get used to it. Just about the first time I sat on it, the thing it was noticeably faster than my road race bike (which is itself an aero road bike and I run a really low and as narrow position as I can get). Unfortunately, my plan to do some TTs this year didn't pan out due to bike unrelated reasons, but, well, next year.
It's all about the legs? Sure, human performance variation is huge and exceeds bike performance variation by far. Same guy, totally different bike, though? The difference is big - you don't even need to tease the data to see it, the difference is plain as day.