Most bindings are either toe cap or convertible (either) and are worn as caps. Caps are superior for my feet, it just locks the boot into the heel cup better and overall has better ergonomics on my feet. This makes riding less fatiguing and board inputs a little better for me.
It's subtle, but since everything is toe cap nowadays, there's no reason for me to seek out or use over the top straps. YMMV.