The 270x is a refresh of the HD 7870. It's was a relatively powerful gaming card back when new, and still counts as a decent entry level gaming card now. It's equivalent to an RX 460 or GTX 1050 of the new cards, to give you an idea of where it ranks. It uses a fair amount of power though, make sure you have a halfways decent power supply.
The 1030 is meant as a low cost upgrade for people with inadequate integrated graphics, and it can do some casual gaming. For just esports games at 1080p or less, it's fine. If all you're going to play is CSGO or Dota 2, things like that, get the 1030. Also, it's a very low power demanding card. It'll work with far less power than a 270x.
In your case, to play such a wide range of games get the 270x. It's true some games will struggle with that 8400 CPU, but at least in everything else you will get decent performance. The 1030 gives you are far narrower range of playable games.