You'll have a LOT more traffic on the Anchorage-Denali section than from Fairbanks, not only en route to Denali, but also to some of the recreational lakes north of Wasilla. That being said, assuming you are flying into Anchorage, I'd probably say to start from there just to acclimate yourself slowly from urban to wilderness. I find it's usually more relaxing to start riding at your entry point rather than have to travel another day to start. (Well, you could fly into Fairbanks, but most folks don't.)
If the weather is clear, you'll also have the view of Denali pulling you on. Try to time your transit between Anchorage and north of Wasilla to non-weekend days to avoid extra traffic. Also, riding early or after 4:00 will let you avoid the bulk of the RV traffic. There are tons of rental RVs in Alaska and the drivers should be watched with extreme wariness.
North of Denali park the hwy has much more of a wilderness feel and less services. It's also only about 1/2 the distance from Denali to Fairbanks as it is from Anchorage to Denali. If you get to Denali and decide you want to stay longer for whatever reason, you'll have better options for getting back to Anchorage (train, shuttles, hitchhiking, etc.).
While Denali is understandably a strong pull, also consider riding the Glenn Hwy east from Anchorage. In my mind this is the prettiest highway in Alaska and goes through a lot of unspoiled areas. It has a lot of ups and downs, though, so beware of that. A great ride would be Anchorage to Glennallen on the Glenn, then the Richardson south to Valdez (another beautiful road, especially from Thompson Pass to Valdez). Then ferry, fly or shuttle back to Anchorage.