Pioneer is utterly hopeless: if your primary concern is warranty performance, forget the Pioneer. Their service facilities are staffed by surly unhelpful people who have been told to obstruct any attempt at intercountry warranty support. When Pioneer left the USA dvd/hdd market, they left it with a vengeance and they are dead set against Americans importing the Canadian units: you can only get service within the country of purchase by presenting a receipt and proof of residence, no trans-shipping allowed.
On the plus side, current Pioneers are amazingly simple mechanically and very robust, with much better than average editing software that does not cause HDD crashes. A DVR-560 is not likely to need service within the warranty period, rendering the mfr warranty moot for most buyers. (There have been one or two reports on AVS of buyers receiving defective Pioneers new in the box, but this is vanishingly rare and would normally be handled by immediate return to the seller for exchange.) Current Pioneers are all variations of the basic DVR-640 design of 2006, which has proved extremely durable and is only now presenting cases of burner wear after heavy use, three years later.
Panasonic seems to have more warranty tolerance for Canada-USA cross-purchases. And their out-of-warranty, flat-fee $130 repair program beats Pioneer by a mile (while repairs to new Pioneers are rare, the company charges $300+ to repair/replace burners on the 2005 and older machines). To be fair, the EH-55 with its TVGOS and other additional features may have slightly higher incidence of breakdown during warranty than the simpler Pioneers, so Panasonic arguably should indeed be providing better warranty tolerance, and they do. Most Panasonic "breakdowns" seem to involve the disc clamp in the burner getting dusty, this can be self-serviced using instructions posted here by member DigaDo, who is very experienced with Panasonics. Other than the dirty clamp issue, we don't hear too many reports of Panasonic EH-series failure during the warranty period.
Both the Pioneer DVR-560 and the Panasonic EH-55 are excellent machines, reliable and well made. If I were you, I would prioritize the machine I prefer over warranty concerns. If you are used to using one brand or the other, stick with it. If you haven't used either brand, the Panasonic EH-55 offers the advantage of TVGOS (until February, at least) and is probably the most popular machine among AVS members. You might also look at the Pioneer 460 at CostCo, which is the same as the 560 but often on sale for much less, especially if "open box". Another option is the new Sony RDR-HX780, which is a Pioneer 560 with a Sony tag on it. This one is often on sale for $229- an amazing buy.