A hard steel will hold an edge longer, but will be harder to sharpen and is more brittle.
A softer steel will need to be resharpened more often, but is easier to sharpen and less brittle.
For like 99% of the population, a dollar store knife will hold an edge long enough and will be easy to sharpen.
I’m too lazy to link because i’m on mobile, but outdoors555 on YouTube recently made a video where he sharpens a dollar store knife and hack away on a piece of 2x4 and the knife stays sharp throughout the ordeal.
So yeah, overall, it’s how you maintain and sharpen your knife that will make a lot of difference.
A honing steel is only helpful if your knife isn’t properly sharpened because it realigns the burr. Just take an extra minute to remove the burr properly and your knife will stay sharp for a while.