I have a lot of experience with both and love them both, but they are different. I also find a huge difference between the Rickenbacker low gain and the newer high gain style pickups (I personally much prefer the more vintage sounding low gain PUPs of the 4001 and early 4003s, but I don't play metal style music). And yes, they do sound very different with flat round strings. I think the early 4003 Rickys (circa 1999) with low gain pickups can sound surprising versatile with round wounds, but few people are recorded doing that.
I agree that an Alembic has more tonal variation. BTW, A good bass that will get you in the Rick department without breaking the bank is the multi-talented Peavey T40, but they weigh a ton! Their value is creeping up as well, but for $750 - 850 they are a great buy.