I don't think much of Kyle Walker and would really prefer Clyne. Walker can attack but defensively and positionally he is poor. I think England's main problems are lack of centre back cover and holding midfielders to shield our defence. Carrick is useful but I think he is more of a passer. I never thought I would say this but Gareth Barry is playing well...
One problem with this debate is that it isn't Carroll who we should be comparing Lambert with. For me, its Rooney. Lambert plays much more like Rooney. He is not an out and out target man and he is happy to drift back into midfield or out to the wings. This obsession with Lambert/Carroll is a bit of a nonsense really. Its like comparing Lallana with Crouch (Crouch is much better in the air by the way!!!). So, the proper debate is should Hodgson pick Rooney or Lambert. I am SO biased that I would go for Lambert over Rooney because he is better at holding the ball up and bringing others into the game, he can get forward and add a huge presence in the box, he will take a good penalty and free-kick, and finally, everybody loves him. Of course Rooney will go.
I don't think Lambert would be picked over Rooney either, but he could provide cover for Rooney. I think he is worth taking on that basis alone.
I know Lambert and Carroll are not really very similar, but they are competing for a place because of the job Hodgson wants them to do: win headers and hold the ball up, which none of the other strikers are good at doing. Given Carroll's injury problems, and Lambert's success in an England shirt so far, I think it would be a miracle if Carroll overtook Lambert now.
Hodgson said as much...he's looking at new players, but they will have a tough job to get past those in place already. Mustn't forget it also comes down to fitness at the time.