I have used them in the past. Both Visa and AMEX.
My experience is that AMEX seems to be easier - often times for AMEX I had to provide the warranty page and original receipt, or invoice, along with the failure mode and often they would provide a statement credit after processing the paperwork.
On our Visa it was slightly more involved - they wanted the warranty page, and the receipt like AMEX, but also a written repair estimate - only then they would process the claim. Often on many electronic items getting a written repair estimate is next to impossible as you need to find a place that can not only do the repairs but will also provide a written estimate for no cost. Many places require seeing the item and so shipping an item to the repair service center can get expensive. Some places required pre-payment before sending an item for repair...
So there are some gotchas - on an item that would be easy to get a repair estimate, pool products should be, it would seem like both companies would be just as easy.
In general I have found AMEX to be slightly easier to work with, but Visa, and Chase for me, is slowly catching up.