Brochas Daf Tes amud beis

The Gemara tells us that Dovid haMelech didn't start saying Hallelukah until he (prophetically) saw the downfall of the wicked. The Maharsha says this seems to contradict what we learn in the Midrash (as quoted in Sanhedrin daf lamed tes) that we don't say Hallel on the final days of Pesach because "HKBH says - my creation (the Mitzrim) drown, and you are going to say Shira!"

The Maharsha therefore suggests an alternative reason for not saying Hallel, namely that Hallel was instituted only when there was a change in the korban brought from one day to the next, which was not the case between the first and subsequent days of Pesach.

This explanation of the Maharsha seems at first sight to leave hanging the Gemara in Sanhedrin; but I have heard another explanation for that Gemara which removes the difficulty once the Maharsha supplies his alternative reason for not saying Hallel.

When Sancheriv's army, which was besieging Yerushalyim, was wiped out by the plague in a single night, we are told it was because the angels sang Shira. If this is the case, why then did the angels not sing Shira to kill the Mitzrim at the Yam by means of a plague? HKBH gives the answer - "My creations (Bnei Yisrael) drown (by the Mitzrim who caused their male children to be thrown in the river) and you (the angels) want to say Shira? No, their death must be mida kneged mida. I Hashem will kill them by drowning."