I'm sitting on the fence.

My experience went like this.
1.Started strapless on one of my regular boards and loved the freedom.
2.Bought a strapped board but wasn't that impressed at the loss of freedom, plus I kept stuffing up when gybing/switching getting my feet in and out of the bloody staps (which were too tight and very uncomfortable).
3.Went back to strapless for a while and worked on getting my gybes sussed.
4.Experimented with moving the straps around, then bought some better staps (Dakine Ultimates)that allowed me the adjustment to have them so that they were very loose and comfortable and so started using the strapped board all of the time and hardly notice the straps now.
Bonus is that you can push harder, get air, jump waves on the way out etc.
5.Just recently started using a strapless board again and love the fact that it feels much more like surfing.
Basically for smaller. cleaner waves and when lightly powered - strapless and
surf the waves.
Larger, lumpier, closeout, onshore type waves and well powered (like this arvo 30kts

) - strapped 'slash and hack'.
IMO if you are from a surfing background just start strapless on any old surfboard, its really not that hard.