First, the SM57 gives a weaker signal, as seen in audacity. Both were recorded at +60dB gain on my Onyx Blackjack, and the Heil comes in just 0.7dB below 0dB.
Top track is the Heil PR31, bottom is the SM57.
I wonder if there is something up with my SM57 as it does seem quite low output. I was mic'ing about 10, perhaps 12 inches away from the sax, aimed at the middle of the upper stack, straight on.
Here are some full clips, Doxy is more jazzy, whilst Endless Night is more for evaluating a slower legato piece.
Heil PR31 vs SM57 by Gallen