Bristol is lucky to have Ashton Court / Leigh Woods on the doorstep (plus lots of other good spots) but they can get pretty dull after you’ve ridden them a lot. Also very good access to Quantocks, S. Wales, and FoD. Brecon Beacons / Black Mountains are good, but not as much riding as the Peaks. From Manchester the Peaks and Pennies are very close, plus all the riding to the north and southeast, North Wales, and the Lakes / Dales up the road too. Plenty of jobs up there too…and cheaper that Bristol.
Ive lived a good few years in both and they are both fantastic places to live. Bristol is a much more relaxed city in comparison….but with far less going on culturally and economically (jobs). Manchester defiantly has the very large, urban feel to it…in many parts of Bristol you can live within 20 mins walk to the centre or 15 minutes on a bike to the countryside.