There’s a whole host of factors that come here, but as a general rule carpeting stairs is the cheaper option, but not always. A standard set of stairs (13 steps) needs around 20m2 of laminate, with costs at the low end around £20 a square metre, so it would cost around £400 for materials.
More expensive and specialist stair laminate would obviously mean that your outlay for material would be more. This can easily be £500-£600.
The price of the best carpet for stairs starts at around £10m2, but expect to pay twice as much for a good quality stair carpet and you will need to factor in an underlay which can easily be around £10m2. Alternatively, you can choose a budget foam backed carpet that doesn't need underlay for around £5-£6m2. Making this cheaper than laminate. But carpet is much quicker and cheaper to install if calling in trades.