Depends on the machine, the price difference & the length of warranty on the new machine.
That said, we had my mom's old Singer refurbished when I took up sewing (she barely sewed 3 things on it before it went in the closet for the next 12 years collecting dust, but there was part of a broken needle caught in bobbin compartment & the timing was off). After the repairman gave it a full work-over, it ran as good as new. When I was shopping for my new machine, I started by looking at refurbished machines, but they just didn't have any that met my requirements so I bought "new" and am not thrilled with it. It came with a NEW sales price, but it was a floor sample. That's all the place sells are floor samples. It seems very suspicious to me & I suspect they probably bought them used & fed me this nonsense line about it being a *benefit* to buy a machine that's already been test driven rather than one in a sealed box. They refused to sell me one in a sealed box, even for a higher price. They claimed they didn't have any more machines in stock except the one that was out, and yet I went back for more thread later that day and sure enough, there was another machine out on the floor.
So I guess the moral of the story is: it's not as important whether it's new or refurbished. What matters is who's selling it to you.