[greentea11]

how do they differ in their reactions to nucleophiles and why?

from the photo i'm comparing the 4 membered ring and the 6 membered ring, so the 2nd and 4th in the photo

Is it to do with the strain of the ring, hence 4 member ring is more strained so less stable, more reactive to nucleophiles?

any help appreciated

[discodermolide]

Yes, the beta-lactone is more reactive. Just look at what is does to the bond angles of the poor carbon atoms, the alpha lactone is even worse!