There is no set answer--either way can work. Do you want the runner for color? Is it to make the stairs more comfortable?

Don't put a carpet runner on stairs unless you are okay with vacuuming on stairs. If you have back problems, you'll be happier just sweeping.

Pros for runner: warm on feet, buffers noise, safer for children and family, add colour, creates cosy atmosphere
Cons: expensive, a pain to clean, can get dirty, more difficult to replace when you tire

This is a personal choice. But I dislike runners on a staircase.

Yes it's such a personal choice but runners do tend to attract dust and are much harder to keep clean. That said carpet will deaden the noise of foot traffic and it's safer if you have kids.

What type of house do you have? Modern or traditional. Modern house stairs tend not to have runners, wood, metal, or glass stairs, and traditional homes, wood stairs. do tend to have runners. I agree with safety concerns mentioned above. So, what type of house do you have? Modern or traditional? and do you have an actual picture of the stairs?

Be aware that if you do not use a stair rod, the installers will destroy the stair treads with their staple guns.

It's a difficult decision, guess you would have to list the pros and cons to determine the answer.