Both brands give good HDD's.... I would go based on the price/model you prefer and the length of the warranty offered.
Currently, Seagate warranty varies from 1 to 5 years depending on the product. (And sometimes depending on where you buy from). OEM may be 1 year, retail (box pack) may be 2, 3, or 5 years. Since you are getting an external drive, your warranty will be in the range 2-5 years.
WD, on the other hand, has differing warranty periods ranging from 1-5 years for external drives also. The WD My Passport Elite & My Passport Studio models are offering 5 years (but cost more). List is available at
WD Support / Warranty Services / End User / Worldwide Warranty Policy and Limitations
. Sorry there's no corresponding table for Seagate.
(P. S. I own several of both brands, and touch wood both have gone well so far....)
In the end it's down to your personal preference... check the manufacturers' sites for specs, and decide