I disagree with you saying they bowled better than the numbers reflect. They both had moments of bowling well, but in general there were far too many loose balls being bowled, awful deliveries to be honest, so England couldn't build up any sort of pressure when they brought on the spinners and all Pakistan had to do was see off Broad and Anderson and wait for the buffet bowling.
That's the clear difference between the spin of the two teams, one team consistently asked questions of the batsman ball after ball, whereas the other team bowled some great deliveries but just as many if not more poor ones. Maybe Tredwell would have been a decent option, at least he can hold up an end. At the end of the day though, England's options are far and few between. Bringing Patel into the third Test showed that England were not confident in their spinners in my opinion and it failed miserably, although obviously not helped by the Stokes injury.