Check the cylinder walls of both blocks first. Chrysler had some problems with castings and it's more on the big blocks but core shift is something to look at. If the 340 block checks out and if this is an engine you are going to keep for a long time, build the 340.
If the 340 block has thin cylinder walls then build the 360. Both engines are from the same time period and either may have good or bad cylinders. Also, if just one of the 340s cylinders is too thin, it can be sleeved and be better than new.
If you're going to experimnent with the motor or try to sell it soon, I'd build the 360. There must be 10 360 blocks for every 340, maybe more.
Bare minimum cylinder wall thickness is 0.100" or 2,5mm. The thrust side has to be thicker, 0.165" or roughly 4,2mm. The thrust side is the cylinder wall that the connecting rod points to on the power stroke, which is the passenger side of each bank.
R.
