The question is whether you can earn more in interest over the 0% period than you are paid in cashback. The top-paying cashback card offers are 4%+, the longest 0% offers are 12-15 months, so these are much of a muchness for basic-rate taxpayers starting out.
Generally, the lower tax band you're in, the better 0% cards become; as you progress further into a 0% period a cashback card becomes more attractive. Don't forget to factor in minimum monthly payments (typically 2-3%) which reduce returns on a 0% card, and the interest-free period (up to six weeks depending on the timing of your purchase) on cashback cards.
To give an example, at the moment the tipping point for me is 6-8 weeks from the end of a 0% deal. I've calculated (roughly) that I get better returns from spending on my cashback card (average 0.65%) after this point.
Other considerations: with a cashback card you don't need a big credit limit whereas for 0% purchases you need a big limit to build up the balance over a number of months. (In general, having large amounts of unused credit available affects your ability to get deals elsewhere but there may be situations in which a large credit limit is advantageous, eg when asking another issuer to match the limit).
And don't forget many cashback cards pay out annually which means you have to keep the card open to qualify, whereas with a 0% purchases card you can put the money into an account which pays interest monthly.
With 0% purchases cards you are exposed to fluctuations in interest rates: if they go up your returns will increase but if they go down you may find you'd have been better off with a cashback card. The good news is, it's "free" money either way.
One final consideration: if you're going to be tempted to spend the pot you build up to clear the 0% card, and leave yourself short at the end, go down the cashback route.