Differences between playing the same game on Steam and Origin?

The differences lie in the services that Steamworks and Origin offer. If you are only playing a game in singleplayer and you have no need for anything special, then they should both be identical experiences. However, if you do care for extra community features provided by Steam/Origin, ask yourself several things such as the following:

Does Origin or Steam offer a better community? Does Steam or Origin have better support for achievements for this game? Does one support cloud saving while the other does not? Am I more invested in Steam or Origin?

Steam has a larger catalog and it's been around for longer, which means it may be worth investing your online presence in Steam rather than Origin. However, if you're happy with the catalog that Origin offers and you want some of the games that are on Origin but not Steam, Origin may be the way to go.

It really depends on how much you care about the external features provided by both services. It's likely better to primarily use one service, so if they are both equal for a specific game, buy it from the service that you have a larger presence in.

the game is the same on both platforms. the prices may vary and there may unavailability for a couple games on either platform.

IMHO for me, its better to play games on steam online because theres better servers and nearer ones for me to play(south africa). but it depends entirely of the game.