I don't think Cameron's program is as sophisticated as John Henry's. She was made for one purpose, to kill, and limited so that she wouldn't become too willful. John Henry was made to learn, with no such limits. He can play with Bionicle action figures. That alone makes him substantially more sophisticated than any Terminator. That he can also play Dungeons and Dragons, and is appropriately excited about rolling a natural 20, hints at a level of free will and imagination far greater than any Terminator is capible of.
Even if that is so, and his program is "bigger" I still think he would fit just fine on a Terminator chip, witih room to spare. It is my opinion that Terminator hardware is way more advanced than today's computer hardware.
Storage space isn't really much of an issue. The bigger problem is number of threads, clock cycles, architecture differences, and program optimization.
John Henry is a highly parallel program designed to run as many threads on many different processors simultaneously
Programs are written for the hardware they're designed to work on. They have to be. If they're written for the wrong hardware, then they won't run. Architecture standards help, but porting a program across architecture standards requires either extensive rewriting, a hardware emulator, or a host program that actually communicates with the hardware for the client program (as with Java). Most likely, in order to run John Henry, a sophisticated hardware emulator is required to simulate his home environment on Cameron's chip. Emulating highly parallel hardware is difficult due to synchronization issues, even on superior highly parallel hardware.
Most likely, the chip wouldn't be able to run nearly as many simultaneous threads as John Henry's native hardware can, particularly when emulating John Henry's native hardware, and a great deal of processing power would go to ensuring that the emulated hardware remains correctly synchronized. This would limit him.
Furthermore, Cameron's chip will not have the raw clockrate that John Henry's servers have. High clockrates produce massive amounts of heat, and Terminator chips lack sophisticated heatsinks, apparently relying on highly parallel processing at lower clockrates. This might not be too bad, if the Cameron's chip architecture is much more efficient than John Henry's chip architecture she can have a high rate of operation completion even at lower clockrates, but much of Cameron's architectural advantages would be lost in the emulation process.
And yes, I am very much overthinking it.
