The Pirelli P4 and the Michelin Harmony are the main-line equivalents, so you should be able to get a pretty good understanding of how they perform. In this size, the Michelin is likely 150% the price of the Pirelli. I'm usually a Michelin person, but in this case, I don't know...it's a close call.
The Pirelli P5 did score pretty favorably in Consumer Reports' last all season tire test (last year). Unfortunately, no Michelin Harmony/Destiny variant was tested, just the HydroEdge. The P5 had some ups and downs, in terms of scores. Its wet performance appears to be second to none. Interestingly, it's snow traction was rated only fair, but it's ice braking was rated very good. It did score very good for noise also.
If comparing cost, and especially cost of ownership, the P5 only scored fair for rolling resistance and good for expected tread life. I think the Michelin Destiny would easily best either of those scores if tested, so it may be a cheaper tire to own, on a dollar per mile basis.
Honestly, I think it's probably a toss-up, and I'd likely lean toward the Michelin just based on my own experience with the brand. Also: are you considering the $70 Michelin rebate in your cost comparisons? If not, that might push you toward the Michelin.