After a while it is possible to discern a persons style, allowing people to know who made which piece. However if people are sensible enough to remain unbiased then their vote should go to the piece that they feel is better, whether that be for technical ability, or even just for the concept and aesthetic look of the piece.
Entry 1: A concept that is often seen from those starting out in graphic design, and also a style that is heavily used and influenced from the TV shows and graphic novels of manga/anime. That said, the concept is there and it roughly follows the rule of thirds (which is a useful guide to use for those starting out in gfx). To improve it I would create a new background, probably keeping to the style of anime/manga. Maybe even going for a comic book feel.
Entry 2: Composition is ok, the lighting is good and there seems to be a decent scene there. It looks like you have applied the image and given the entire piece a sharpen, which has spoilt the depth. I would go for the smart sharpen filter, and only sharpen it enough to achieve what you want done on the focal. Don't be afraid to erase the background back though, varying the opacity of your eraser to improve the depth. Also there are a couple of blown out spots on the fractals (the pure white areas) which are detracting from the focal. Tone them back a bit by say placing a splash of colour over them (clip mask other parts of the fractals?) and it will bring the attention back to the focal. The piece is a bit monochromatic too, however it does seem to work. Maybe see what it would look like with some other colours in it though?
Overall though my vote goes to entry two. Although it does have a few issues it does feel more "complete", and to my eyes I can see a scene/story to it, which I can't yet see with entry one.