I have been using the 8" and 10.25" pans for almost a year with an induction cooktop. I am considering the 12-3/4" one, too. They do occasionally go on sale here at Amazon for less than the usual prices. I wish they made a shallow 2-1/2 quart, 8" diameter saute pan with lid.
Other reviewers have mentioned what makes them so great, and I agree. I think there is something about the ceramic/titanium material embedded just below the surface that makes it cook so much like stainless steel, but without sticking, of course. I rarely use SS skillets for browning anymore, unless I want to make a sauce from the "fond" that builds up in the pan.
The one thing that would make them PERFECT would be a flared pouring rim. This may be difficult to implement due to the materials used. I don't know, but it would be great to have. I find that when I pour from these pans, I have to be ready with a slightly wet and soapy dishcloth to quickly wipe the side/bottom, as liquid WILL run down the sides and then the bottom. If I don't wipe immediately, and the pan is really hot, the liquid will begin to harden/set.
This effect would be even more so with a gas or hot radiating electric cooktop if the pan is returned to the burner without wiping, and cooking continues. Then you will then have to later exert some unnecessary "elbow grease" to clean.
Bar Keeper's Friend works great, btw.