You won't be able to recreate the experience you had playing Mass Effect. I'd say instead of trying to find something that is most similar to it, try to find something within the same genre that is similarly high quality. The Mass Effect story would be garbage if it wasn't executed so well, if the writing wasn't so good, if the characters as well fleshed out..etc.
My recommendation would be Stephen R Donaldson's Gap Cycle. It's five books long, and some of the best space opera out there. It's exceptionally well written.
Any recommendation for the Gap Cycle needs to come with a warning of course: the first book, and part of the second, are brutal reads - they are very well written and move right along, but they are filled with misery and pain. Rape, beatings, and torture are pretty much the name of the game for most of the first book. They are still very good books, but be prepared for some nasty stuff.
The story starts very small, it's basically a character study of two people. The series opens up a bit in the second book as we get more characters and more of the world and hints of the greater alien threat. From the third book through the end it's an epic space opera with a wide cast of very well drawn characters - each of whom have distinct motivations, lots of political machinations, space battles, a super-killer-cyborg, and a very real alien threat to wipe out all of humanity.
The series is some of the best in the genre.