I completely understand what you mean- and I can cop some pretty good tones/playing styles on any bass but as you said there are somethings so fundamentally different that I'd need a Rick/Jazz to really nail.
Well it basically depends on the bridge being used, wood selection etc. If you have a rosewod jazz bass than you will have a harder time to get to that geddy lee bass sound but other than that, you can get by.
With Jbasses its really basically about the next things - Maple vs rosewood and 60's vs 70's pup spacing. Everything else is basically hardware related which can be modified with aftermarket parts if you so desire. Ok neck thickness is also a thing but that really only exists to make your hand more comfortable while playing. Some prefer thickness, some can't live without a slick thin fast neck... Up to you.
IMO, if you are not a collector it makes no sense to have multiple Jbasses at home. You will realise you will main one anyways and shelf the rest. Unless you are rich. Otherwise maintaining a number of bass guitars with strings is an expensive thing.
Let me tell you something else - if you really dig the geddy lee tone, get yourself a geddy lee bass. Jbass afterall is the more versatile instrument of the two. Then sell your am std and save some more money and go for the rick aswell.
Now, I don't know what music you play mainly and what are your future plans with bands and your sound expectations and that may also affect your decision.
You won't go wrong with neither of the listed bass guitars but if playing versatile music is more your thing rather than sticking to one specific genre with your only band the Geddy Lee bass will bring you more bang in general.
I myself am a professional bass player and would love to have a Rick too, but only as a specific bass for specific things. Making it more of a side project. Believe me, I brought Yamahas, Musicmans, Ibanez basses etc. etc. to the different bands gigs and rehearsals but always got the best compliments for the tone and "fitting" of the tone while playing on a jbass or pbass.
My best advice would be to find a store with a live room, take your band with you and try them both with a band. Whatever lifts your hair higher is the thing you want
