I'm a Carrick fan, he is no Pirlo and never was. Pirlo's attacking vision is something else, he is unflappable under pressure with amazing dribbling ability at zero pace, and he is a dead ball master too. Of course Carrick is better defensively, but overall it's Pirlo by a distance.
Alonso is a much better comparison. Same position and style of play, same weakness. In fact the last time they met while both were in their prime was the Madrid CL games. Kagawa/Welbeck silenced Alonso, while Carrick played a very defensive role and had a few
great moments (sent Evra clean through and Varane should have been red carded, headed pass for Rvp, nice skills to escape pressing) and no mistakes vs genuine top-class opposition.
I don't know if they played in the Moyes Bayern games because that season has been wiped from memory.
And just as much as Carrick sucked vs LvG's Bayern, Alonso was ripped apart by Klopp's Dortmund. And Carrick has had tons of big European games: Inter 2009 and Chelsea 2011 were probably his best.
I really don't get the Fletcher argument. They're very different players, and Carrick is much rarer and for me personally someone who controls most games is better than a normal box-to-box midfielder. (Vidal is box-to-box too but his passing is extraordinary and he has shown the ability to run the whole team's passing by himself).