Is there much of a difference in size between a 360cc and 380cc?

No, most patients who undergo breast augmentation surgery will not notice  a significant (or any) difference with 20 cc different breast implants. Generally speaking, the best online advice I can give to ladies who are considering breast augmentation surgery ( regarding breast implant size/profile selection) is:
1. Concentrate on choosing your plastic surgeon carefully. Concentrate on appropriate training, certification, and the ability of the plastic surgeon to achieve the results you are looking for. Ask to see lots of examples of his/her work.
2. Have a full discussion and communication regarding your desired goals with your plastic surgeon. This communication will be critical in determining breast implant size/type/profile will most likely help achieve your goals. 
In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. For example, I have found that the use of words such as “natural look” or "C or D cup” etc means different things to different people and therefore prove unhelpful.
Also, as you know, cup size varies depending on him who makes the bra; therefore, discussing desired cup size may also be inaccurate. Again, the use of computer imaging has been very helpful during the communication process, in our practice.
3. Once you feel you have communicated your goals clearly, allow your plastic surgeon to use his/her years of experience/judgment to choose the breast implant size/profile that will best meet your goals. Again, in my practice, this decision is usually made during surgery, after the use of temporary intraoperative sizers.
I hope this helps. Best wishes for an outcome that you will be very pleased with. 
 

There is not much difference between the two sizes. After a full recovery, it would be very hard to differentiate between the two sizes. If what you want is perkier, larger breasts, then it would be better to choose the bigger size of the two just to be sure. Discuss this with your surgeon as he/she would know your condition best.