I had a lovely ride today - even seeing the Sky team bus at Eddleston.
The cycle path from Peebles to Innerleithen is excellent, offering a worthy and flatter alternative to the two road routes. You can pick it up by proceeding on the main road to Innerleithen. You can pick it up by following a signpost up a wee lane to the left. This takes you on to a pleasant tarmacked path through the woods. This has a tricky and tight double hairpin down a steep slope. Didn't like that bit. At this point you are right next to the main road again - so you can also access the path here.
It then dives under the road - a bit frightening first time as it's quite steep on concrete and the tunnel is very dark. The next bit is a bit windy until you get on the old train trainline proper and for a while the surface isn't tarmac. I managed it fine with 23 mmm tyres though. The path is then delightful, with good sightlines and next to the river.
The path is mostly quite narrow so it's probably best to pick your time if you want to go briskly. I went at 9.30am - there were only a few cyclists and dog walkers near the villages. Didn't see any horses and not too much muck.
So I'd recommend it, particularly if you want to avoid traffic and don't fancy the hilly south road.