I agree and disagree with you both.
Gerrard has been very good before for England. The performances so far aren't very good, they're great. He is arguably the best player in the tournament right now. In that sense, I agree with Uppercut; and I usually argue against Englishmen calling their own players rubbish. Gerrard in the last 3 big tournaments for England has been one of the main sources of goals - either scoring or assisting them - mostly playing out of position. How can that possibly be seen as bad?
Where I disagree with Uppercut, slightly, is the CL05 run. Truly, others besides Gerrard had a hand in that run - often important performances (Garcia, Hyypia+Carra, Alonso). But, he was still comfortably the most important player and in a sense, as much as is likely in football, carried Liverpool. It depends what you think about him, but I think it rightly justifies his legacy, he was fantastic and it was fairy tale run.
Why he hasn't been the same, or as great, in England is that he has rarely been in the same position or same role for England. For the majority of his caps he has played outside his best position - instead, on the right, or holding, or on the left. Even when he was given captaincy it wasn't with the responsibility he has now. As Carragher said during the Ukraine match; I think Gerrard finally feels like he is the leader; and he thrives on that responsibility. Before, you had many alpha dogs in Terry, Rio, Beckham, Lampard, Rooney and he never had the same role in that team as he had in Liverpool. Gerrard is probably more likely to shine in a team that would rely on him - a team like Greece - than one who treats him as the 3rd or 4th rung.
IMO, that's why he was rarely Liverpool's Gerrard when playing for England. Now, he is looking the closest to it. Unfortunately, for England, many years too late. He should've been made captain after Beckham and should've been told it's his team. None of England's other players had/have the capacity to take a team on their shoulders and thrive like him.
I am really, REALLY, looking forward to the Italy game. I think England will target Pirlo and Italy will try to target Gerrard. De Rossi has already come out praising Gerrard and calling him his idol. They know how good he is. English fans are just finding out. I've built him up a lot but if England go far it'll be in large part because of Gerrard.