Thanks for not taking this personally. I wish I could quantify verbally what makes his art distinctively better. Part of it is that he's tapped into the zeitgeist of iOS styling - the flat look, the muted colors with a heavy dash of grey, the minimalism. That styling has heavily influenced current app design across the board.
Looking at yours on the Play Store, some things stand out to my untrained eye:
- Drop shadows on the title.
- The trees don't look clean (and I have no idea how to dig into that).
- The end scene fonts don't look sharp - they look kind of comic sans.
- The configuration is accessed via buttons, instead of the standard Android styling of the "..." button.
- The icon's person graphics are both too detailed and not detailed enough - they are in an uncanny valley of "eh".
- There's no cohesion of colors: there are multiple shades of green; multiple colors of buttons; multiple shades of blue. Multiple shades is fine, but for UI elements, they are like different colored trim on a house for the same things - window sills.
If you have a friend who is into graphic design, have them write you a critique.
It also turns me off, hard, when apps have exclamation points in the title or the "Free" word. It signifies cheapness for some reason.