Shield drop in melee has 3 Y increments where it'll trigger platform drop but not far enough down to dodge. In PM there are 4 so the range is larger, but the average is further down (the idea being that an average unmodded controller is more likely to dodge on 1 or both notches in melee than it is to perfectly drop on both sides). More controllers as a whole are probably able to shield drop on both sides in PM, but with a controller that drops on both sides in melee (uncommon/modded) there's a good chance it'll be harder to shield drop with that controller in PM than melee by default.
If your controller is on the upper end of the shield drop range in melee, where it works in melee but not PM, you can compensate for that by using the in-game analog calibration (plugging in or hold start+X+Y) to tweak the notches' Y positions. -0.6625, -0.6750, and -0.6875 are the melee increments that drop. If you get -0.6875 on a notch in melee (can see in debug physics/input display) it likely works in both games, but the other 2 probably just angle the shield in PM. If that's the case, press and slowly release the control stick towards an upward direction before plugging in/resetting the controller. If it's worse at dropping with the SW notch in PM, which is more likely in this case because SE notch tends to be lower than SW on GC controllers, you probably want to press NW/NNW before calibrating.
Press->release->calibrate makes use of the small amount of loose zone controllers tend to have. It's also helpful in reverse for controllers that work better in PM than melee (drop in PM but dodge in melee) by calibrating with a downward direction when playing melee. Pressing and releasing up for one that works in melee but not PM is usually enough to get the right calibration, but if the controller has little or no loose zone you may need to maintain a very very tiny amount of upward nudge when you calibrate rather than fully letting go. Not enough to visibly move it, just a bit of pressure to the underside of the stick where you first feel resistance.