In my subjective experience and despite potentially misleading DCR values, the SH13 (measured inductance: 6.85H) is closer to a L500L (measured inductance: 6.4H) than to a L500XL (measured inductance: 9,4H). But it has a higher Q factor than both. IOW, it has a more focused harmonic peak.
These specs make it brighter than a XL and give it scoopier low mids than to a Wilde L500L.
For me, the closest Bill Lawrence to a SH13 might be the P90 sized L550...
IME. YMMV.
EDIT - Like with all passive pickups, the sound of a SH13 depends on the guitar used, with its scale, but also on external electrical parameters: resistance of the pot(s) , input impedance of the amp or pedal used, stray capacitance of the cable.
If a SH13 is too shrill, pair it with some pot(s) of lower resistance or mount some resistor(s) in parallel. If it's too bright, rise the capacitive load, either by using a longer cable, either by putting a low value capacitor from hot to ground. Or apply both solutions, since higher capacitance rises the Q factor and might require a lower resistive load.
A stupid 100pF cap from hot to ground would already make a 500L or a SH13 a lot closer to a 500XL EQ wise. But it's not forbidden to experiment with higher values, from 100pF to 1000pF (1nF) or higher.
FWIW: trying a capacitor from hot to ground costs a few cents and takes a few minutes if the cap is connected to the output jack by alligator clips... And the same strategy can be used to diminish the resistive load (if you have two 500k controls and want to hear what it would do with 250k controls, just put a 270k or 220k resistor from hot to ground of the output jack - or just lower your tone pot. LOL).