MT4 is basically the "original" MetaTrader software ... MT5 is "new and improved", but comes with some drawbacks (like most new softwares).
MT5 has much better testing and optimization tools available, including more detailed output (for EAs). MT4 is more rigid, but generally regarded as more stable, largely because it's been around longer.
Then, of course, each one has it's own mobile app on iOS and Android, and is mostly a matter of personal preference.
Note that there are a lot more EAs available for MT4 than MT5, but that will probably continue to balance out as time goes forward.