Definitely the one without the bevel! You're absolutely right that the bevel clashes with your lovely hand-drawn style.

I don't think it's hard to see the roads or the red icons, though the grey ones get lost a little against the background. Could you try adding a small black stroke around the grey icon, or maybe a glow, to make them stand out? Not sure how that'll work, since the icons are pretty small. Could you try a different colour instead of grey?