Switch flats and rounds from one bass to the other

I just bought a Fender Jazz Bass that came with flat wound strings. My current Squier Jazz Bass has round wounds that I put on last year. I'd like to switch the strings, moving the flats to the Squier and the rounds to the Fender.

Do I need to set up each bass from scratch, or should I leave the saddles untouched? I don't know if my situation is an easy, one-to-one switch, or is it a little more complicated?
 
Depends on what rounds and what flats you're talking about.

That said, every string change should be followed by a simple 3-step setup.

Once the strings are installed and tuned up to pitch...
  1. Check the amount of neck relief, and tweak the truss rod as needed.
  2. Check the overall action, and adjust the saddle height as needed.
  3. Check the intonation, and adjust the saddle positioning as needed.
 
The ‘witness’ points made when installing a string are the bends made at the bridge and the nut. They would have to be exactly the same between two basses to effectively swap ensuring tonal and tuning integrity.

But, heck yes you can do it although I would recommend new strings and setups.
 
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I just bought a Fender Jazz Bass that came with flat wound strings. My current Squier Jazz Bass has round wounds that I put on last year. I'd like to switch the strings, moving the flats to the Squier and the rounds to the Fender.

Do I need to set up each bass from scratch, or should I leave the saddles untouched? I don't know if my situation is an easy, one-to-one switch, or is it a little more complicated?

Whenever a string comes off or goes on a bass I check (and adjust if needed) the truss rod relief, saddle height, and intonation. Even switching to strings of the exact same brand/model/gauge can need require setup adjustments. Probably something about releasing and reapplying tension to the neck.
 
Rounds "last year"? Is that 2 weeks ago or a year ago? While I am fine with dead roundwounds (don't like the "piano" sound of fresh rounds), a modern player would typically replace rounds pretty often.
 
Rounds "last year"? Is that 2 weeks ago or a year ago? While I am fine with dead roundwounds (don't like the "piano" sound of fresh rounds), a modern player would typically replace rounds pretty often.

The previous owner said he bought the bass (Fender) six months ago and set it up then. The Squier I had set up with new strings last spring (April or May).