I'll tell you why I personally dislike Origin. TL;DR at the bottom.
If have issues, you'll have to deal with EA support. Yeah, pretty much any experience you have with anyone's technical support will be terrible, EA's is even worse. I can't stress that enough.
Origin itself is an inferior program. Any time you reinstall Windows, you have to reinstall origin and it wants you to redownload and reinstall all your games. It doesn't matter if the game files are RIGHT THERE and are perfectly fine, it doesn't care. There are some work arounds that involve moving the files, starting a download, and moving them back(for each individual game) but the point is it shouldn't be needed. Steam instantly detects installed games and you're good to go, done. No BS.
If you have your games and Origin on a drive that is left intact after a reinstall, you can load Origin and it will run and appear to be just fine. However, it will inexplicably prevent multiplayer games that connect to a server from functioning, with no error message or any hint as to that being the case. Even checking Origin's tech support forums that fact is no where to be found. With Steam, just run the executable as an admin and you're done in seconds.
What do I like about Origin? Well, I guess free games from time to time, but sometimes they screw even that up. (Syndicate without the expansion available ANYWHERE, wtf?)
Maybe less overall server downtime, but that could be just a result of not using it nearly as often.
I still would not tell someone to not play a game they are interested in because it requires Origin, I would just advise to use Steam for your general use and only use Origin when you must.
TL;DR
Origin...
-has much smaller game library
-is inferior to Steam in most ways
-requires more effort and time to set up after OS reinstalls
-is said to be more invasive and collects more information than it should
-suffers from more random and unknown problems that prevent you from playing games for no apparent reason
-EA's Tech Support is in a league of it's own in the being shitty department
-lacks services that Steam provides such as easy to access forums, ratings, reviews, etc.
-updates far less frequently
-does douchebag stuff like Origin only games even though it means less sales for the developers
-refuses to accept they came too late to the party and offer little incentive for use. It's like Google+ and Bing. There are better and more popular alternatives, so what's the point?