Pioneer Elite vsx-14 enough for hdi-3800? Alternatives?

Your jbls are very sensitive at 92db and shouldn't need a lot of power. Otoh they're rated to go down only to 37hz, which isn't super-low, so it may be they're just not as bass as their predecessor. Synergy is critical, however, so you could very likely get different results with another amp, tho you could also add a sub.

fwiw, for my bedroom system i recently replaced my 20-year old pioneer elite vsx80 with an anthem 740. the anthem is serviceable, and has the modern features like room correction, arc, etc., but to my ears doesn't sound as good--flatter and less musical. whether this is because of synergy or because the pioneer is an overacheiver i know not. undoubtedly, you can find something better, but i'd give a close listen to your current pioneer before upgrading.

@szejna, i'm no tech wizard but i do know that frequency response measurement is an imperfect science and that other factors like dispersion, and dynamic range could make two similarly-spec'd speakers sound very different. i was curious enough to read some online reviews (e.g. audiosciencereview) of your jbls, some of which suggest that for low bass they would benefit from a sub--again, you might get better results with a different amp, so i wouldn't hesitate to experiment.