97 is probably faster and busier. Along 97 you can stop at Shanko (an fun, old, town to explore....as long as they haven't "rolled up the sidewalks" for the year yet).
197 has a fairly steep grade dropping down to the Deschutes River and then back up the other side. But, if you wanted to explore the Deschutes river (go rafting, drive down to Shears Falls, check out the White River, etc), then that would be the way to go.
If you truly had a day to burn then I would suggest 97 to Shanko, then backtrack the few miles back to 197 and go that route north.
Enjoy the journey.