For the most efficient pedal system, both me and my stoker use Shimano road SPDs and shoes with ultra stiff carbon soles, those with a 3K carbon weave and not those with carbon infused nylon. When we need to walk it's a minor inconvenience to be walking with cleats. The excellent power transfer more than make up for the slight inconvenience. The pedals I use are Shimano Dura Ace 9100.

I have had Speedplay Road, Frogs, and Syzrs on the MTB. I've since gotten rid of all Speedplay branded pedals and went with Shimano exclusively. It's day and night difference and I'll never go back to Speedplay.