Google Maps gives the 101 route 40 more miles and an hour more.
The Narrows bridge may be slow, but so is I5 south toward Olympia. But WSDOT (and Google Maps) is good at keeping track of traffic on these roads. On GM you can ask for routes at various times of the day. Afternoon rushhour out of Tacoma can be slow both ways.
101 along Hood Canal is scenic, but long and curvy. I wouldn't recommend it if you are in a rush; it's better to take your time and stop for meals, beach walks and state park visits.
16 is mostly divided highway, with a narrower median near the junction with 3. 3 continues like that through Bremerton. It widens through Silverdale, and becomes 2 lane north of Poulsbo.
I would use the Narrows Bridge unless realtime traffic indicates that it is really slow.
