I'd definitely go by train. The National Express buses can sometimes have stops in other cities along the way for up to an hour and a half or so, which can be a pain if you just want to get to your destination.
Also, although trains can sometimes be delayed (rarely by more than a few minutes though) there is FAR more likelihood that the bus will be delayed due to traffic conditions. I got the bus back home from uni once, and due to bad traffic conditions, I missed my next bus (had to change in London) and had to wait two hours for another one.
I had a little look. To travel from Edinburgh to Leeds will take 3 hours on the train and a one way ticket will cost you around £11 (these trains are usually run by Virgin or GNER, which both have really nice trains). To get the National Express will take anything between 7 and 11 hours (depending on which time of day you leave) and will cost £37.
I know which I'd choose!
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