340 and 360's are identical in size as far as external dimensions. One isn't going to fit better than the other.

340's are usually harder to find and cost a lot more money than a 360. The price difference to rebuild either one is going to be pretty much the same. I have seen rebuildable 340 engines priced as high as $500.00. I bought my 360 core for $50.00.

If the car is going to have mild gears and an automatic I would use the 360 since they produce better torque all things being equal.