SUP's are delightful. They give anyone and everyone something wonderful to do on the water, like hiking on the water. For experienced surfers, SUP's open up breaks that are too fickle for longboards.
Then main drawback to SUP's is when novice riders dominate a surf break. SUP's make catching waves easy for anyone and their riders tower over conventional surfers in the line-up. The boards are monstrous when out of control in the soup, a real danger.
What is wonderful about inflatables is storability. New models, shaped by surfers, appear daily. No matter how good an inflatable, they will never have the same agility as a high performance stick. They will stretch, deflate, shrink in cool water and soften under a hot sun.
Now that I have a 36' sailboat, I have been shopping for a high performance, surf-specific inflatable. Rigidity rules. AE's Stiffy with aluminum side stringers seems promising as do shapes from experienced sailboard and SUP shapers like Naish and C4.