I have two bows at the moment with carbon limbs. Both have wood cores. I have no experience with foam cores, which is a whole different dimension to your question.
The first is a one-piece Schaffer Silvertip longbow, and the second is a takedown Hoyt Satori recurve.
The Schaffer is a 42# 66" longbow, which I bought to shoot in longbow competitions that require wood arrows. My wood arrows are about 10 gpp. This bow shoots them at a ho-hum 166 fps. The interesting thing is that I have a 40# Toelke Lynx 66" longbow that shoots the same arrows at the same speed, without any carbon in the limbs. I really can't tell any difference in shooting the Lynx or the Silvertip, so I am fairly indifferent between the two. Some longbow competitions require one-piece, so in those I would obviously shoot the Silvertip, but with an extra 2# and carbon limbs, you would think it would perfrom better than it does compared with the Lynx.
I have several 40# recurves to choose from, including a Black Widow, a Bob Lee, and a Rick Welch Dakota. The BW and the Bob Lee are about 6 fps slower than the the Satori, shooting the same arrow. The Dakota is about 2 fps slower. The Satori will shoot a 7.9 gpp carbon arrow at 192 fps, whereas the BW and Bob Lee come in at about 186 fps. In fairness, I think the Satori was designed to shoot a low gpp arrow, whereas the other two were not. The Dakota was designed to shoot a fast arrow, but the Satori is a little faster with slightly less aggressive design features.
So in my mind, the jury is still out as to the benefit of carbon limbs. My friend and mentor Rick Welch has stopped putting carbon in the limbs of his bows, because in his opinion it adds expense without commensurate benefit. I had one of his earlier recurves with carbon, which didn't seem to shoot noticeably better than bows with non-carbon limbs.
I'm beginning to think that you need to have specific expertise in carbon limbs to get the most out of them, which Hoyt seems to have. Just putting carbon in limbs without understanding the underlying mechanics and engineering doesn't seem to add much to the performance of a bow. But, as I said before, my experience is very limited.