I've noticed that the ATEMEGA328P U version doesn't function quite like it should
Please explain exactly what you mean by "doesn't function quite like it should".
Are the chips properly decoupled? Process differences between individual chips/lots can render them more or less sensitive to improper or insufficient decoupling caps. The P U chips are more recently produced, if I'm interpreting the date codes right. Maybe they got a die shrink or something?
Electrolytic caps suck for decoupling. They have too much ESL and ESR. Ceramics are what you want (tants are ok too, but they cost several times as much and explode if you connect them backwards - I only use them in special situations, not run of the mill decoupling ). Buy a bag, you'll use more 0.1uF ceramic caps than any other single part.
One on each side. And make sure that AVcc and Vcc are connected (I have seen tutorials where this isn't done).