I find that for riding Fixed Gear on the road clipless pedals are easier to engage/disengage, more secure and comfortable than clips and straps.

A quick clip-in as the off side crank comes up I'm off w/ no drama or wobble as can happen when one leans down to tighten an off side strap.
No awkward loosening/re-tightening for traffic controls, just un-clip at stoplights proceed and re-clip.
To get similar retention to clipless straps have to be very snug, not as comfortable for extended FG rides.
The efforts to climb a grade on FG can be considerable, the RPM required to descend exceeds what most riders produce: clipless gives the security for both.
I've used clipless on all of my road bikes since the 1st Look pedals, not having to remember what retention system I'm using makes riding simpler.

-Bandera