Moving between MAC to PC

You will not have any problem at all.
Collect a folder with all the file & the .aep. ( On the menù - File - Collect all files _ All )
That's all.

True, but if they have a newer version of AE than you have you might not be able to open the project when they hand it back, assuming that is the workflow. They will also need to have any third party plug-ins that you used, if any, and visa versa.

Another thing that might cause a problem is that if you are giving them a mac formatted hard drive they won't be able to read the files on a PC unless they have macdrive or similar software. I have macdrive on my PC and use a mac-formatted hard drive to exchange files with my mac at work and with files from my friends macs and it works great but it's about $50. You can format in FAT32 and both mac and PC can read that, but there is a 4GB file size limitation.