What are the typical issues of a passive crossover that are solved by the JBLs? I've heard (or read) that everything else being equal active monitors or better than a powered monitor but I don't know why.
The JBL LSR as far as I know are a two-way analog active speaker with a 4th order acoustic crossover. I really doubt they would sound overly different from the passive equivalent.
What you do get however is better efficiency. Tweeters tend to be more sensitive than woofers so you can often drive them to the same SPL with half the power or so. You're not wasting any power to resistance losses. Same with baffle step compensation, which is especially optimized in a powered monitor where you need to adjust it based on room or location.
Also, consider that most power is centered around 50 watts to 400 watts or so. If the amplifier powering that section is clipping, it could potentially "reach the tweeter" for a passive speaker (on paper... not sure if that's ever happened to you in actuality). By bi amping you're not letting any of the woofer's clipping reach the tweeter. At the very least, it might sound a bit better as the woofer's natural inductance might reduce the clipping "effect". At best you're protecting your tweeter - mostly relevant for high powered applications mind you.
This last part is only relevant for extended listening periods. As a woofer voice coil heats up, its electrical behavior may change. Now a lot of woofers, especially metal cones (which are not used in the LSRs btw) require notch filters in order to keep cone breakup controlled. There is a thread here on the first page discussing cone breakup if you're interested. Now a passive notch filter assumes a certain impedance at a certain frequency in order to work correctly. But if the voice coils have heated up, it is possible that the passive notch filter might work at the wrong frequency - and you end up accidentally hearing cone breakup at high power levels. An active filter should filter the frequency, not dependant on the driver's thermal conditions.
With all of the above said, the best thing about the JBL LSRs
isn't in the crossover, but in the EOS waveguide which gives a very smooth integration to the excellent JBL woofer in terms of off axis reflections, and wide sweet spot.
Otherwise, I'd say the biggest advantages of active crossovers are:
High order digital Finite Impulse Response / Linear Phase filters - Like those used in the Beolab 5 and NHT XD for example. The LSRs do not have this.
No need for huge inductors. This is more important for 2.5, 3, and 4 way speakers than it is for 2 way speakers.
