depends on what you're cutting (length of cut). all foams are different but typically your rigid foams do well with a hot knife or razor knife. a nice clean cut can be had by either, not sure about a table saw or circular saw. got a feeling the teeth are too aggressive and a wide kerf once you take into consideration the tear out.
worked for a place that did prefab foam insulated steel panels, that's all i did was mess with foam all day long. not the paper backed panels, just huge sheets of generic styrofoam type foam. cut bevels for windows, door frames, squared edges, sanded the panels flat prepping for stucco sealer.
the cheapy dollar type utility knives with the snap off blades work good because you can extend the blade out to get through 3-4" thick material. using a straight edge and applying very slight force to bow the blade you can get it to hug the straight edge.
never used a small diy hot knife so those may not work all that great. used one around 12ft long, was a two person job and like anything else there's a knack to it. can't go too fast, go too slow and it burns and wallows out the edges. done right it leaves a hair line through the foam and the heat melts and seals the edges just like a factory edge (vs the crumbly edge typically achieved by scoring/snapping).
if it was softer foam i'd opt for a turkey carving knife (like poly foam). hot knives won't work so well with foam cushion. good luck.