I can’t believe that route takes you up to Mam Nick on the road. What a horror show bit of route planning.
Also the stretch of the A624 above Little Hayfield is busy of a weekend and, if I read the route correctly, involves a right turn on a half-blind bend – I’d be very, very careful on that section. Hopefully they’ll marshal that turn off, but it’s not something I’d do unless I really had to.
Then again, their road route – next day I think – tends to take people over busy main A-roads on a summer Sunday. The Snake Pass, if I remember correctly, around mid-day. Wouldn’t touch it.
Anyway… I’d take whichever bike you’re happiest with and bear in mind that you’ll be slogging up a steepish road climb halfway round if that makes any difference to you choice.
Edit: sorry if that seems a bit negative, but they do the same routes every year and the road one in particular seems badly thought out for a mass ride on a summer weekend in the middle of the busiest National Park in the UK.