Have you ever had a not-at-fault accident ? With 3rd party you and the other insurance company sort it out, and it can take time, they can try to force you to go to their choice of repairer et cetera.
I've been told legally you don't have to use their choice of repairer.
Furthermore they will make you wait until they're client's car is repaired before authorising your repairs.
Comprehensive, they take care of it for you, you get your car fixed.
Also as mentioned 3rd party fire/theft is often capped at 5K, read the fine print.
And you already know what happens with an at-fault accident