I started from the 320, then stepped up to the 330. There was a clear upgrade. Checking out from Yamaha’s brochure, I found the 320 has smaller speakers and fewer sensors to the keystroke strength, while they share the sound source, tone generator and amp system.
Then, I went on to test the 340 and the 370. They are another step-up from the 330. According to the brochure, the 340 and the 370 share the same hammer sensor system, the sound source, tone generator and amp/speaker system. Those are the elements usually affect the sound and touch of an instrument. However, they gave quite different impressions in tone quality. Believe it or not, I like that of the less expensive 340 over the 370, which give less tone-sustain in the treble and too much brightness to my ears. I think it maybe cause by the better frequency response in reproduce the famous Yamaha brightness, and it may be modified by it’s internal EQ system (if there is one).
I was only paying attention to the aspects, which affect the quality of sound and touch as replacement of an acoustic piano. I did not look into any other features. If you they are important to you, you may find the info on line.
Out of those four models, the winner to me is the 340. I do not see the reason to pay more for the 370 for something almost the same as the 340. For a lower budget, I would take the 330 as well. The 320 did not impress me as much. Talking about the price, I only glanced the price tags on the instruments. They were list prices, which do not mean that much any way. You may find the street prices from you local dealer.
Hope this quick review helps.
BTW, in terms of imitating the acoustic piano, digital pianos have come long way from the early 80s. However, as much as I like many digital functions, I still would not seriously practice on them. I am not comparing them to the cheap commercial grade acoustic pianos. I will take an acoustic piano from 5-10K range over the most expensive digital piano.