The Picaxe can communicate a few ways, you haven't spelled out exactly what you mean by "communicate". ie is it enough for one Picaxe to turn on a led when told to by the other, or do you need file transfer with error handling?
If by "Modbus" you mean using the Modbus protocol I think that would be way overkill for a college assignment. The protocol reference document is 121 pages long. They do have "Modbus over Serial" as well but that's still quite complicated.
Using RS485/232 would be easy though, just hook up a couple of transceivers and come up with your own simple protocol.
BTW, neither 485 nor 232 are a "protocol", they specify the hardware parameters of a serial link.