I used router bit one time and after the bit warmed up it started melting the foam which stuck to the bit, heating more foam which melted into a glob which caused not the bit to cut the foam but the spinning hot glob of foam cut (if you can call it that) to wander wherever it happened to go.
I used a band saw, jigsaw and table saw a lot, but it is probably more dangerous cutting foam than wood because, again the foam wanted to melt with any friction with the blade and then it would want to stick to the blade. The table saw was the most useful, but also most dangerous. end of ramble......