In reply to Stuart (aka brt):
Depends when youre going and whether you want to have views/stops on the way.
A470 is nice, with plenty of scenic stopoff points - if you've never done it before and you're not in a rush go that way - but it can be tiring as it's mainly single carriageway winding roads so overtaking is difficult. Not too bad if you're travelling at midweek quiet times (late evening, early morning) but a pain if youre driving midday on a sunny sunday.
A49 is usually easier - wider, straighter and often dual carriageway roads, less tourist traffic.
I used to use the motorways if I wanted an easier drive but nowadays the A49 route is much improved and the motorways can be awful around B'ham I would definitely use A49. Wouldn't use A5 to ByC though. I'd go up towards Wrexham and hit the A483 & A55, or via Llangollen and Ruthin.
Post edited at 14:21