I would sign up with both--after all, it's free and miles in the Delta program don't expire. I always look to credit to the Alaska program first if it's at all possible, but sometimes it's not possible. For example, if you're flying on an R fare with Aeromexico, Delta awards credit but Alaska doesn't.

I also lived in Beijing for 3 years and having the Delta program was really useful because none of the Chinese airlines have partnerships with Alaska. China Southern and China Eastern both credit to Delta (provided that you're not flying on a non-awarding fare class, which unfortunately was the case for me often). Additionally, flying with Aeroflot (one of the best ways from Beijing to Europe) won't credit to the Alaska program but it will credit to Delta (usually at 75%, but that's 75% better than nothing). Domestic business travel in China over the years eventually earned me enough credit with Delta for a free domestic US flight, which isn't much but it's certainly better than nothing.

When it comes to status, you're better off going for status with the airline you fly the most. There is some reciprocal status given to Alaska flyers on Delta, but it only matches the Silver level of their program. This doesn't get you much--upgrades in theory but not in practice, and first checked bag free on domestic flights (one extra bag on international flights). You get the same thing on Alaska as a Delta Silver--they give you the same benefits as MVP.

One final thought: watch for promotions. Both Alaska and Delta offer double miles promotions and other bonuses throughout the year. Even though you may normally prefer a given program, you might want to switch to get a bonus.

In my case, I have flown more than enough for the past several years to get status, but I don't fly enough with any particular alliance to qualify. This year, I didn't even pay for most of my tickets (I used miles). I can assure you that the sun still comes up every day even though I don't have airline status and I feel free to go for the lowest possible fare without regard to airline alliances. Points have been devalued so much, and the bar has been raised for status to such a high level, that it's not really worth chasing either.