The difference is that Caesar was deified despite there being no claims to him performing miracles. Jesus was deified because of the claims and because the claims hadn't been refuted.
If Jesus didn't do the miracles, then why don't we find books or letters denying them: say, an interview with blind Bartimaeus, still blind despite the Christians claiming he'd been healed. Instead we find a lot of pseudogospels which were written in the centuries after Christ, some with good intentions, some with bad. These read more like legend, and were excluded from the new testament canon because they were not eyewitness testimony or based on such.