Thanks, Bill, the picture tells me a lot.
Essentailly, the Elan would feel (weight/size) more along the lines of the StingRay Five. Wood varies, but in all maple it may be just a bit heavier. The Essence would be closer to the Jazz, physically, though the neck will be noticeably wider, as a five-string. They can get get slightly neck heavy with the small cutaways. I don't know your size, but if the MusicMan feels like a BIG bass to you, the Elan would also. The Essence is closer to the Jazz overall.
Control-wise they're essentially the same, and they'd have a noticeable 'family resemblance' tone-wise. The difference would be in the woods' effect on the tone (all-maple is brighter than a maple/mahogany blend) and in the pickups' shell/coil sizes: The bigger AXY's (the Elan) would 'sense' bigger lengths of string vs. the smaller MXY's (the Essence). Think of this in terms of your MusicMan's tone vs. the Jazz Bass. How much of a difference would be subjectively down to the axes in question, as wood just varies . . . Alembic pickups are very neutral and ultra-clean. Think studio monitors instead of home stereo speakers. You WILL hear yourself doing things you never heard before, and these dang things have a way of MAKING you play better, 'cause you can just hear more. They aren't especially 'bassy' sounding to the uninitiated. They can also make your favorite amp suddenly sound like a cheap radio in some cases.
The bigger difference to me is the single preamp vs. double preamp. With the double preamp, you can set the blend of the two pickups relative to their tone and output; think of it as a two-channel mixer between the pickups and the output jack. Alembic pickups have a moderate output which allows you to run your pickup heights strictly by personal preference. You then open up the back cavity, and each preamp has a trim pot to set each output separately: Set them identically, neck-heavy, bridge-heavy, whatever you want the arrangement to be vis-a-vis your fader knob out front. The Essence would, in effect, allow you to set the output 'globally' only.
In my experience (I own a P/J Elan Five and a Spoiler Five) I would have to have the double preamp setup. With it I set the blend exactly where I want it when the fader knob is at 50/50.
This is one more of Alembic's genius moves: All bass pickups change tone in a subtle fashion as you raise/lower them to the strings, as well as output. The trim pots in the preamps allow you to set the blend/outputs exactly as you want to hear it, a feature not available on anything else I can think of.
I'm demanding, set-up wise, and the deluxe laminates in the Elan (plus the double preamps and that terrific price IF it's as clean as it looks) make this a no brainer IF it were ME: I'd take the Elan. But I would not presume to answer for you. The triple purpleheart lams with the ebony fingerboard would make this VERY stable set-up wise. With the one-piece bridge, double truss-rods, and the adjustable nut, they're a breeze to set up.
In terms of 'cutting through a band': Your MusicMan is certainly the PBass of five strings, but can get fat sounding, and the PRS is beautifully dense: Light sounding they're not. The Jazz is a Jazz, but if you've sold off a bunch of fives, and you're looking at another one here, I don't imagine you spend a lot of time with it.
Finding your spot in the mix, irregardless of guitar or amp, is a skill not easily learned, SO dependent on the whole band and you learning your spot. It could certainly be done with the axes I see in your picture, but after thirty years of playing and who knows how many axes, I can tell you there is nothing like an Alembic, and nobody like the Wickershams.
I can also tell you they're not for everybody. Lots of guys do a lot with a lot less, and couldn't hear the difference at gunpoint. Don't understand why they need a 'coffee table' bass instead of an old Fender. The genius of the axes is lost on more than a few, and that's OK.
Me? I flirt with other things from time to time, but I'm just RUINED by these things. I think you would be too.
J o e y