Both routes look fine to me, the only real bit of road on mine is through Tilford, I think it's mostly byways and forest tracks. For a ride like this I like to make good use of the orange highlighted routes on OSM cycle maps via RWGPS (of which this is one), these always seem to be specifically chosen and uploaded by cyclists.
I did consider going south through Thursley and Hankley but it can get pretty sandy as Ed mentions as well as busy with walkers. There is a really cool route round there though, round the bottom of Hankley Common. The whole place is a big crater looking thing where I think they filmed skyfall. Just a bit sandy though.