I've watched and been a fan of both shows. Having said that, Outlander is like watching a full-on movie each week. The writing, acting, and cinematography is breathtaking. Believe it or not, Outlander is not cheesy or cheapened by the concept of it being about a time traveler. In fact, that aspect of the show is hardly recognized. This is NOT your run of the mill sci-fi program.
Here is the biggest difference...Downton Abbey is a night-time soap; a fun, gulity pleasure. Outlander is in a different stratosphere. It's like nothing that's ever been on TV before. It's brave, daunting, awe-inspiring; like watching cinema every week on the small screen.