You gotta want the 340 to do a 340. If the 360 is in your lap, ..... it is a great street / strip performer. The bennifits of a 360 are 20 extra cubes and it's all in stroke , which gives more torque, the thing that gets you going.
Engine power peaks sooner because of this and the power output match a 340's with great ease. You'll really build it no different. It just doesn't need to rev higher to make the power.
The bigest issue for most people is finding a 340. Then the next big issue is the expense of the 340 block alone. For the price, you can get a entire 360 for less money.