I have bikes with: clipless, clips and straps, and flat pedals. Here are my thoughts...

The roadie has clipless and I'm certain that I pull up when I'm sprinting or standing. More power is good.

Mountain bike has 50/50 flats. I like being about to put a foot down, but I miss the extra power when I'm trying to get over or up something. At least a couple of times each ride my foot will come off the pedal because I don't have enough pressure on a pedal. So I'm doing a decent job not fighting the other leg, but I'm only using one leg at a time.

Commuter bike has clips and straps. This is a nice compromise for getting extra power while accelerating but I don't have to change my shoes when I get to where I'm going.

I can definitely accelerate better with clips than with flats. Once up to speed, I think I'm more efficient with clipless, but I don't think difference is huge.