They are the same language! I only ever use the Processing libraries from Java too. There is no speed difference just from that change.
It comes down to LWJGL vs JOGL really. I’ve seen an LWJGL backend for Processing. In fact, it was almost the Processing 3 default, and may still be coming. Still, while there are good reasons to switch because JOGL development has stalled, there’s unlikely much speed difference in communicating with the GPU.
As for Processing not being good for shaders, I’d love to read the reasoning on that! Shaders run on the GPU - there’s little reason why Processing vs Java vs C would be any different there.
Do try and keep the number of PGraphics down by reusing them. Without seeing your code I can’t really say more than that though.