Les Paul or Jazzmaster; depends what sort of tone I want. I use virtually the same hardware and electronics in all my guitars (two humbuckers, one volume, tune-o-matic and stopbar bridges, 24.75" scale), so any difference in tone comes purely down to construction; the body style/mass and the neck join. Seems much smarter, to me, to just let the Les Pauls be the thick-sounding ones, rather than trying to make Jazzmasters sound thicker with particular pickups, or vice-versa.
Of the two, I couldn't choose. One can't do what the other does, at least not without completely changing how I spec out and wire up my guitars.