May sound odd but I think the England ODI side might do better without Pietersen, that of course would be so if England had separate squads/teams.
Cook hasn't done much wrong in ODIs, my main worry is it appears England think a change of captaincy will fix all and are ignoring the other shortcomings in the World Cup - selecting Test players which is why they were tired
, picking players like Yardy and Wright who ain't good enough (maybe for Bangladesh), picking and not using players like Tredwell until the World Cup was at a critical stage, poor all-round play and other problems which won't be "all fixed" by appointing a new captain.
Broad for T20Is is a weird one, but then who cares about that format, it's not as if there is much scope for major tactics within 20 overs.
Of course one danger I always fear when appointing someone who's played under the previous captain is that they have 'learned' their captaincy by copying their predecessor. If Cook just bowls his main bowlers for 3-5 overs then gives a back-up bowler five overs and then makes a complete shambles of it, how will that be any better than Strauss? Until England FINALLY work out that taking wickets is kinda key and "getting through the 4th and 5th bowler allocations" is not really a (clever) tactic, we'll remain the decade or so behind the rest that we are now.
We also need to come to terms with the fact that Australia didn't win the World Cup three times in a row by "luck", we need to get over the idea that luck is a big player in our results. We've been dire in FIVE World Cups in a row, nothing to do with luck, all to do with selection, captaincy, approach and the same things that saw Strauss ousted. We copied the model of central contracts, frankly it's made no real difference. We beat the aussies in 2005 because Flintoff played a blinder and we had four bowlers firing to their two, and few batsmen didn't get runs. In 06/07 we hit earth with a bump, by 2009 the aussies were a pale shadow of their former selves. Besides improved performances and results against the aussies, we're still mopping up the weaker sides and doing well below par against the rest (Sri Lanka, South Africa and India)