If you fly enough to earn status that gives you a good chance at upgrades, you should probably think about doing the FF program of the carrier you fly in order to get those upgrades and other elite benefits. Although Alaska and Delta give upgrades to each others' FFers, they are at the bottom of the priority list, meaning that outside of unpopular times for business travelers and FFers to travel, upgrades are very rare.

Alaska does have better reward redemptions, including flights to Hawaii, so you might have to decide how improtant "free" tickets are for you. You could credit just enough miles to DL for status (whatever is the maximum tier you can earn) and put any excess into your Alaska account, but check their rules about the expiration of miles. Also learn what fares earn how many miles in each program, so that if you have a flight that earns few miles in one program, credit that flight to the other FF account.