Welcome to the forums Troy.
A couple of things to consider before jumping into the purchase of an expensive Aztek double action setup. I looked out on Testor's website, and it really looks like the A320 uses the same interchangeable nozzles as do the more expensive Aztek double action units. I assume the A320 has some sort of a needle adjustment behind the trigger.
If that assement is correct, upgrading to a double action Aztek, won't change your painting quality. Your abilitity to paint fine lines will not change either. The only benefit that you would get from the change would be that you can vary the paint flow from the trigger while actually in the process of painting. If you are very skilled with an airbrush, this will give you the abilty to do some cool effects that would be more difficult compared to doing them with a single action unit. Far and away the vast majority of model building situations will not greatly benefit from a double action AB vs. a single action AB and even then you need a fair degree of proficiency to see a significant improvement by upgrading to double action.
You didn't mention exactly why you desire to upgrade. If you are a very skilled airbrush artist, get really good results with your A320, and have simply outgrown its capability, then upgrading to the double action unit might not be a bad idea.
On the other hand, if you are still new to the game and the results of your A320 are not matching your desires, the problem is probably due to lack of experience. The skill of airbrushing really is an art form and to become truly proficient beyond laying down a smooth coat of paint (something which can be done effectively by any airbrush, no matter how cheap) is a skill which can take years to develop. In this case, you might yourself better served by cutting your airbrushing teeth on your current setup and upgrading when you have truly outgrown it. By then you would also have more experience to make a better informed decision about a new airbrush.
Lastly, since you used the word "cheap" with respect to your A320, perhaps the thing clogs regularly, drips paint, or just doesn't paint nice. If this is the case, upgrading to a double action Aztek would leave you using the same paint nozzle system used by the A320, which in turn means that any sort of usage problems like clogging, spattering, etc. would follow you to your new airbrush.
If for example, you are hoping for better fine line control, stick save