What (if any) is the difference between Ideal implants and Mentor Memory Shape implants? Which is better?

There are many differences between the two implants you mentioned; principally, the "ideal" implant is a saline filled breast implant whereas the Mentor implant you mentioned is a silicone gel-based implant. Personally, I think that careful selection of plastic surgeon and careful communication goals are  the two most important "factors" when it comes to achieving the desired outcome with breast augmentation surgery.   The specific breast implant manufacturer and even type of breast implant are far less important factors, in my opinion.  All of the FDA approved breast implant manufacturers provide good products.
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” 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 (and the attached link, dedicated to breast augmentation surgery concerns) helps. Best wishes. 

Ideal implants are a new type of saline implants, with multiple shells and saline fill.  MemoryShape is a silicone gel implant.    There are many differences between the two.  I've attached a link for you.Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons.