The Photon uses a mini-SIM, the S4 uses a micro-SIM. If they both used the same size, no, there's no reason not to move it from one to the other.
You CAN get a cutter and adapter on eBay, so you can cut the SIM to micro size to use in the S4, then put it into the adapter to use in the Photon, if you want to be able to switch back and forth.
Depending on your carrier, a new SIM may cost a few dollars, or they may give you one for free.