It depends on what you are attempting. The one with no boarders makes it feel more immersive however you lose the paper feel of the lower one.

If you have some kind of custom design mechanic, or if the player will be reminded that it's paper, then use the second one for more style.

I think they both look cut out. The one with the border has more of a little big planet feel to it. I like the one without the border though.