This is really easy. You don't even need both calculators. All you need is the TI-Graph Link software for both calculators. You need to download the software for the TI-83 and the TI-83 Plus. Once you have both softwares downloaded and working, you're set. First, open up both softwares. Second, create your program in the software for the calculator that you have. Once you're program is working correctly, highlight the entire source code and copy it. Next, go to the other TI-Graph Link program and paste the source code. Save the program and you're done! That's it. Now you have one program that works for two calculators.

Note: If you use the TI-83 Plus software to make your program, make sure you do not use TI-83 Plus-specific words like Archive/Unarchive. These commands are not recognized on the TI-83, and thus, the program won't work for the TI-83. Just try avoiding using those two commands in BASIC programs that you want to work for both calculators.