A 360 would be cheaper and provide more torque, max power a few hundred RPM's less than a 340. Max HP levels are near identical.
Is there a HP power level you wish to achieve? Like, so you can say "I have *** HP!"
What gear ratio and/or cruise RPM can you live with?
Do you like a auto trans or a 4spd to drive?
Rear end size, AKA 8-1/4 or a 8-3/4 has a big price difference. The smaller sized rear can still hold a good amount of power while the larger one can hold copious amounts. Do you need to spend a lot for a rear that will never see the half of it's potential?
From these questions, your answers will direct me to some answers.
Otherwise, you'll just get 100 opinions, 33% will make no sense and 50% will be a waste of money. Something easy to spend on the internet with bologna advice.