In rubber bridge, when should you "lead your partner's suit rather than your own?"
In general, you are correct not to lead that ratty heart suit with a bad hand. Instead lead DT hoping to catch a quack in dummy and partner with some cards in the suit. With luck you might get in again with a heart to lead the suit a second time for partner.

That being said however, the opponents bid game aggressively; in MatchPoints it might be better to try the heart 3 with the goal of not giving up an overtrick, rather than defeating the contract.

With the second hand, not playing MatchPoints I definitely lead the heart suit; or if the auction had finished 1NT - 2NT - 3NT I lead the heart because opponents have bid a minimum game. However in MatchPoints, with the opponents having bid to game strongly, I am leading the heart suit only because every other possibility is worse and so the heart lead is least likely to give up an overtrick.

Update:
As pointed out below by Ruds, if the opponents play CBS or NMF over 1NT in this auction, then the failure of responder to do so is a loud denial of a 5-card spade holding. In this case only a spade lead (highest spot usually, but dependent on leading conventions) can be considered at all vulnerabilities and styles.