I travel both routes each summer. Usually going east on 20 and west on 2.
As stated hwy 2 has more traffic and congestion. SR 20 is more scenic,has less traffic
and truck traffic is almost nonexistent going over the mountains. Once in Eastern
Washington you will eventually have to go south a bit and enter Spokane on 2.
There are several ways to do that, all good. My favorite is to go to Republic on 20
then go south and take the Keller Ferry to Davenport on 2 then East. Whichever
way you choose to go it will be mostly 2 lane, not much traffic and scenic. If coming
from Vancouver Island, take the ferry from Sydney B.C. to Anacortes WA. You will
be on 20. Follow the signs and enjoy the ride.
https://www.wsdot.wa.gov/Regions/Eastern/KellerFerry/