Personally I like the second image as the 3rd one makes the characters look like they are floating when stood but you would need the jumping image to have a black outline under the feet of the character to make it look right in the air.
I think it makes it more dynamic and with the lower resolution pixelated look improves it vastly. The first image is still good though
I think the hearts and stars at the top would be good with an outline too. Think Terraria but not as much outlines
and I think you have got it spot on then.
Having said that, you can't please everyone and people will also like image 1 and 3!!! It's a hard call to be honest because 1 and 2 are both good, just think 2 gives that bit more polish
Have a look at this Terraria image, this is a bit overkill with the backgrounds having an outline too but I think you are on to something with a bit of both in image 2
https://lh5.ggpht.com/5FKIFvWn5kNQvPLM4stjbVhWDuZkHB-ztk6oWP31dbvo7e9VrmoHpQYmzZcXFpj64g=h900
EDIT:
Also your forum icon has just caught my eye and on seeing this now I would definitely say an outline for your character as when he is animated the sword and shield are lost in the background. I would say try the black outline on your forum icon of the animated character and see if that makes a vast difference