I can't compare synthetic vs cedar shakes, but I just did my house with heavy cedar shakes. The nicer asphalt roofs (I think they called them "dimensional") would have ended up being close in price because we would have had to have plywood decking installed.

And then when you're done, you have fake shingles. :/

Asphalt shingles are the cheapest roofing you can get.

The roof will also become hotter as the shingles retain heat.

Synthetic shakes are more costly than asphalt shingle and can be relatively heavy depending on the material used.

Another alternative to cedar shakes could be metal shakes such as Metro Shake II. I just re-roofed from asphalt shingles to metal (Metro Shake II) and the difference in temperature is palpable.

In New England there are many more shingle choices including pressure treated and/or prestained white cedar shakes. I'm sure the same is available in the northwest probably with red cedar.

Here is a link that might be useful: pressure treated shingles and shakes