I agree that price isn't the best criteria to judge an oil, but VALUE is. And I'll distinguish that very specifically.
Amsoil is a high-end high-quality synthetic-based line of lubricants; it has many direct and indirect competitors. With that in mind, you need to understand that "synthetic" lubricants are much better at longevity of service, but not necessisarily better at protecting your engine. Look over many of the hundreds of UOA's here on this site. There are PLENTY of "conventional/dino" oils that turn in stellar UOAs. I personally posted a UOA for my neighbor's '05 6.0L PSD F-350 that had outstanding UOA results for a 5k mile run on conventional Rotella 10w-30. It was so good, that we're trying 7.5k miles next; and we'll keep pushing it out until a UOA shows it's no longer advisable to continue service.
Now, we need to revisit our grade-school math concept of "association" for this next point I'm going to make. It's greatly important to understand that ANY lubricant eventually gets contaminated, and has it's additive package depleted, to a point where it's unadvisable to use the fluid anymore. It doesn't matter if it's group II, III, IV or V; they all eventually get into a state where they should no longer be used. Therefore, the protection level they offer is eventually compromised. Therefore, at some point, ANY lubricant would return a bad UOA. The point here is that a synthetic and a conventional oil will both give appropriate protection of the engine; it's just that synthetics are capable of doing it longer.
Synthetics also offer some extreme enviornment abilities that a trump a conventional fluid. But, be careful here, because quite often these attributes are embraced for situations that NEVER come up. Unless you live in the true artic region, where -15dF ambient temps are routine, then cold pumpability isn't really a big deal. Further, extreme heat isn't as big a deal as you think, because (presuming your cooling and lube systems are functioning as designed) you engine won't tyically see over 210dF anyway. I agree that synthetics perform better at these extremes, but since you RARELY IF EVER SEE THIS HAPPEN, it's an added benefit you'll not likely capitalize on.
So this leaves us with lubricant life as the main selling point of synthetics. Here, synthetics typically do outlast, and therefore outperform, dino oils. Each engine design and regional environment contribute to the overall longevity of a lubricant as well. But overall, it's very fair to say the synthetics will easily outlast dino's, given near identical operating arenas.
With that in mind, the question of "better" becomes one of value, and not price. Value is what you get for your money, not what you pay. If you can consistnetly use UOAs and extend your drain intervals, then synthetics will pay off in the long run, and therefore would be "better" financially. If you're going to run 5k or 7.5k mile OCIs regardless, then synthetics are not a good value at all, because you cannot dollar-cost-average justify the expense.
It's up to you, not us, if synthetic is better, based upon your use. Regarding your initial question: in no way do I believe that Amsoil will be "better" in the long run. Proper maintenance routines will be "better" in the long run. How you achieve that is a matter of personal preference. Many people use synthetics with the false assumption that they are protecting their vehicle better, yet they still change their fluid at "dino" intervals. UOAs clearly show there is no advantage to this practice.
Synthetics and bypass filtration are tools for making lubricants last longer, not equipment.