I have the D3100 so might be biased. The swivel screen isn't a biggie for me as I prefer to have my eye to the viewfinder 99% of the time, but I can see it might be handy sometimes. The range of the d3100 is fantastic for low light shooting, and the VR lenses help with this, the D5100 would add another stop and a bit, but with a wall to lean on, mine will shoot in full night anyway without flash.
Both will do 1080 movies but more options on the 5100. However, both are great for making mini clips like watching your mate fall off a bike, but completely useless for stuff like recording the kids Christmas shows as the clip is limited to 10 minutes on both. If you want a camcorder for this stuff, the Nikons don't help.
Since the price difference is still pretty big, I don't think the D5100 is worth it as a first DSLR unless you're minted. As others have said, the non Nikon/Canons can give you a fantastic camera too for a bit less. My film camera was Pentax, but the K-r was a lot dearer last year so I jumped in with the Nikon and love it.