Doesn't the post-war P1 have an aluminum alloy frame, as opposed to the wartime P-38's steel frame?
Yes, although I've heard of no significant complaints borne of that.
In theory, the P1's aluminum frame means it's less tolerant of a hard life of shooting +p ammo. OTOH, they were made in peacetime with all due care. The late-war P38's could be dicey too, and there's some anecdotal reports of cracked frames in the steel P38's as well.
Honestly, other than the difference in collector's value, and the chance of getting a really rough late-war P38 I think it's a wash. European loads trend a bit hotter than SAMMI spec stuff, so if it's going to mainly digest 115gr WWB and similar bulk FMJ loadings, I wouldn't worry at all.
As a shooter, I'd rather have the P1.