What would promotion at your current job actually mean? Would it be a new role with new responsibilities, or just a job title? Would you get more money?
Did you go for the other job just to leave this one, or to go that one? Meaning, will it be more of the same, or will it mean more challenges, more responsibility, useful experience?
Unless there's something that definitely puts you off the new job, (I turned one down in similar circumstances, because it would have been a fairly grim commute, and the office had no natural light, which would be a big issue for me, plus although it was a payrise, the commute would have wiped that out in petrol costs,) I would probably cut your loses and go.
Even if you do get the promotion at your current place, if they've overlooked you for years, they're likely to expect you to be eternally grateful for whatever you get. Plus they'll know you aren't really convinced about moving, so know they can get away with taking you for granted in future.
In the end, only you can make the decision, but I'd weigh up all the pros and cons of staying and going - I've been pushing for promotion mostly because it would be some acknowledgement of all the things I do, but with us, it would just be a job title change, from sys admin to senior sys admin. It wouldn't really change anything; I wouldn't even get a payrise, just be on a payscale with a higher upper limit, but as each grade covers a range of about £20000 and overlap by several thousand, it wouldn't make a practical difference, as I'm not at the top of my current grade.