What procedure would be best for nasal valve collapse?

Your question is one of the most important questions in the nasal surgery process - how is the patient supposed to know which plan is the best when two surgeons propose what seems like very different options? In my opinion, it comes down to the consultation. I'll explain what I mean.
Your consultation is the critical time where you can learn about rhinoplasty and get your specific questions answered. I personally feel that if the surgeon does not really spend the time to answer your questions, then perhaps that is not the right doctor for you. You need to be able to trust that they will look closely at your concerns and not apply a "cookie cutter" approach to your problem. In your case, I think the question that you are asking the RS community is an appropriate one for each surgeon - "why do I need rib if I have septal cartilage?" or conversely, "why do you think septal cartilage will work when others think I might need rib?". These questions are very specific to your case, and their answers should help you make an informed decision.
A little bit about rhinoplasty and septum vs. rib cartilage. In my opinion, rib is the most powerful option and has the ability to correct almost any nasal problem, including nasal valve problems, if applied correctly. Septum is preferred for its thinness and for avoiding additional cost and additional surgery, but there is much less of it available, which might limit the options available in a given surgery. You also mention that the nose will be larger if rib is used - this may be true, but is not always true. I would ask for an explanation or even to see examples of what this might mean in your case.
Picking a surgeon is a tough and very personal decision. You want to entrust your case to a board-certified surgeon who has expertise in nasal surgery at the very least. Beyond that, make sure to ask your detailed questions, and go with the plan that makes the most sense to you. Best of luck to you, I hope this helps!