Hi S.,
I definitely agree that the plane sounds like a MUCH better option. But, it may really depend on where your son is in his development re: his insistence on independence.
I traveled by plane with my baby boy when he was 8 months old, which was an absolute dream. And, then I traveled with him again at 17 months old, when he was what my husband and I affectionately describe as "possessed by a demon".
At 8 months old, we brought plenty of toys and books and I breastfed him (I recommend a window seat) under a cover-up/shawl during take-offs and landings. It went incredibly smoothly!!
At 17 months old, we also brought plenty of toys and books, but he had reached the "down", "down", "down" (imagine that repeated 5,000 times and you'll have the idea!) stage where he didn't want to be on our laps and wanted to be "down" to go explore everything (which we all know is not a good thing when the seat belt sign is on). After several "tantrums", and walks up and down the aisle, when permitted, it was a definite eye-opener for us. So much so, that we canceled a trip we were to take about two weeks later and decided either no more plane trips until he's three (or through his current stage) or no more plane trips without buying his own seat and putting him in his car seat...
I'm not sure which stage your baby is in at 11 months old. But, you may want to factor that into your decision.
Our son was still very laid back, didn't fight being held, and would "go with the flow" at that age. So, the plane would still have been a good choice for him.
I hope this helps!
Good luck in whatever you decide!
D.