As others have said, no, the two bikes will not handle the same, although they may well steer quite similarly. Trail differences seem to me to have the most influence on the steering feel of the bike. Steering effort and "weight", self-centering, low-speed wheel flop... stuff like that.

Your weight distribution is going to be different, and this has a huge, (maybe even primary,) influence on the overall handling of the bike / rider unit. Front and rear centers, bottom bracket drop, stem length, handlebar size and shape... all of it matters, to varying degrees. The degrees of variation also vary, from rider to rider and from bike to bike. There are some rules of thumb, that are mostly true for most riders on most bikes most of the time, but that's about the limit of what can be predicted from a geometry sheet.

This is all just opinion, based on my having owned and ridden a lot of different bikes over the years... I've never built a frame. So take it with as much salt as you prefer. It is a fascinating subject, and fascinatingly subjective.

--Shannon