[jyl]

Many Yakima accessories can be used on Thule racks and vice versa. Including the baskets. For the racks themselves I like Yakima because of the round bars. And because they are an Oregon company. (Started in Yakima WA, then moved to Arcata CA, now just west of Portland OR.)

Edit: More complete thoughts on Thule vs Yakima:

Thule is headquartered in Sweden with the US local HQ in Connecticutt, Yakima is headquartered in Oregon.
Thule is the larger company, $800MM/yr sales, sells globally and makes various RV, towing, trailer, etc products in addition to roof racks. Yakima is a smaller US-centric company, but I think it has more market share in the US.
Technically my opinion is both companies make fine stuff. Both companies' accessories mostly mount on each others' rack. I have a Thule roof pod on my Yakima racks. So if you like the Thule pod but the Yakima basket, you can "usually" do both.
The main difference between the basic racks is that Yakima has round bars while Thule has square. The round bars allow accessories to be rotated, to conform to a curved roofline or for less drag when not in use. The square bars better resist unwanted rotation, in the few cases where that's an issue - kayak rollers is the example most cite. (Note that if you tighten the Yakima mounts snugly, wind force will not rotate them.)
Cosmetically Thule seems to have a bit more silver whereas Yakima tends to be all black.
I know some of the people at Yakima. The head of product development of Yakima is a bike racer, restores antique Vespas and Lambrettas, his kids come over and play sometimes. The CEO is a family friend. So I am somewhat biased to Yakima. But I buy all my Yakima stuff retail (used when possible) so its not like I have ever asked for or gotten anything free from them.
I think there is a bigger choice of used Yakima stuff, if that matters.
All else being equal, I do tend to buy Yakima to support a US company. Sorry livi.