Google is full of information on this. As Hans Passant said, Form controls are built in to Excel whereas ActiveX controls are loaded separately.
Generally you'll use Forms controls, they're simpler. ActiveX controls allow for more flexible design and should be used when the job just can't be done with a basic Forms control.
Many user's computers by default won't trust ActiveX, and it will be disabled; this sometimes needs to be manually added to the trust center. ActiveX is a microsoft-based technology and, as far as I'm aware, is not supported on the Mac. This is something you'll have to also consider, should you (or anyone you provide a workbook to) decide to use it on a Mac.