Which implant option is firmest and has a round shape?

Choosing breast implants is not simple, and you should do your research, but shouldn't choose an implant without the advice and help of an experienced and board certified plastic surgeon.  There are too many factors that determine the breast implant outcome, and the implant is only one of them.  Among the three breast implant makers in the USA, Allergan's 410 style in my experience is the firmest.  That style does NOT come in round - these are shaped implants.  The proper way to choose implants is for your surgeon to take measurements of the breast and also determine the skin thickness.  Based on these measurements, you will narrow down the choice to implants that will fit your contour.  If you have several choices, you can certainly choose the firmer one if that's a consideration.

Firmness will depend upon how tight the skin envelope is and what size implant you use, but over time they might relax and become looser.

Thank you for the question. Generally speaking,  the type of implant used may  determine the final outcome for some patients undergoing breast augmentation/lifting surgery, especially if the patient does not have significant covering breast or adipose tissue. For example, most surgeons feel that silicone implants have a more natural look and feel than saline implants because silicone gel has a texture that is similar to breast tissue.
Each patient differs in the amount of breast tissue that they have.  If a patient has enough breast tissue to cover the implant, the final result will be similar when comparing saline implants versus silicone gel implants.  If a patient has very low body fat and/or very little breast tissue, the silicone gel implants may provide a more "natural" result.
On the other hand, saline implants have some advantages over silicone implants. Silicone implant ruptures are harder to detect. When saline implants rupture, they deflate and the results are seen almost immediately. When silicone implants rupture, the breast often looks and feels the same because the silicone gel may leak into surrounding areas of the breast without a visible difference.  Patients may need an MRI to diagnose a silicone gel rupture.   Saline implants are also less expensive than the silicone gel implants.  Again, generally speaking, the patient seeking a “firmer” breast feel, saline ( learn about overfilling also) or higher profile silicone gel breast implants may be indicated.
My best general advice for patients seeking to undergo breast augmentation surgery 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're 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 which operation and/or 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. I have found that the use of words such as “natural” or "C or D cup" or "firmer" etc means different things to different people and therefore prove unhelpful.
 Also, as you know, cup size varies depending on who makes the bra; therefore, discussing desired cup  size may also be inaccurate. The use of computer imaging may be very helpful during this communication process.
3.  Once you feel you have communicated your goals clearly,  allow your plastic surgeon to use his/her years of experience/judgment to suggest 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 evaluating the patient's breast size, shape, symmetry in the upright and supine positions.
I hope this, and the attached link (outlining the differences between saline versus silicone gel breast implants), helps. Best wishes.

Thank you for your question.  Generally speaking cohesive silicone gel implants will feel firmer than saline implants.  There are many styles of round breast implants from low profile to moderate profile to high profile to ultra high profile.  In my experience the high profile implants create a more projecting "ball shape "that you mentioned.  Please consult an expert board certified plastic surgeon.