It really depends on what your needs are. My simple answer is THULE, if it earned itself a THULE logo it means they really stand by the product and it should last you a long time. THULE bought out Sportrack which basically took over all of their lower end products. That being said there are some Yakima products that are very well built as well, but also some that I would not recommend.
If you are looking for a roof box definitely consider both brands, Yakima's skybox line is comparable in price to Thule's ascent line, and has some extra features (stiffer lid, metal support bars). If you have the cash to drop on a high end box, stick with Thule (Atlantis, Spirit, Boxter). Another company to consider for roof boxes is INNO, they use a much better plastic than anyone else and make nice low profile boxes which are great for skis www.rv-inno.com.
If you are looking for a base rack (crossbars) and have nothing on the roof, a Thule or Inno system is superior to Yakima. The fit you get with them is just so much better. If you have side-rails and just need crossbars, All 3 make great products for that.
Pretty much everything else is just coke vs pepsi between the two brands. Thule's fork mount bike racks are better, Yakima's upright bike racks are better, ski racks are about equal, etc....
I know I can get carried away talking about roof racks, but If you have questions about anything rack related feel free to PM me.
hahahaha i didnt need THAT in depth of an explanation, the vagina isnt really a goddamn box... and i sure as hell dont know why id stick my nose in it.- Evan.S