Filling a crack keeps water out, not the line itself
Filling or sealing a crack is meant to stop water and debris from working their way into it and making it worse, not to make it disappear. The line stays visible, just closed instead of open. That is a reasonable trade when the crack is tight and cosmetic, and it does nothing to address a crack that is moving because of what is happening under the slab.
It is also the cheaper and faster of the two paths, which matters when the crack itself is not the real concern. Keeping water and salt out of a shrinkage crack before winter does more good than the appearance of the line ever costs you.
Cutting the section out leaves a seam instead of a line
The other path trades one kind of visible mark for another. When a failed panel comes out and gets poured back, what you are left with looking at is a straight joint where the new concrete meets the old, and a color difference between two ages of concrete sitting side by side. The joint reads as a joint rather than as a crack, which is most of the point of doing it that way, and the color gap narrows as both sides weather without ever closing all the way.
This path makes sense when a crack is not just cosmetic, when a section has settled or one side sits higher than the other. Filling that kind of crack does not touch the ground underneath it, so the same movement usually comes back.
What actually decides which path fits
A tight, level crack that is not moving is usually a candidate for filling. A crack where one side sits higher than the other, or where a section has settled, points at something happening under the slab rather than the surface, and filling it does not touch that cause. That distinction is worth a look, not a guess from a description over the phone.
Getting the color as close as it can get
New concrete simply reads lighter than concrete that has been outside curing and weathering for a year or more, whether or not integral color was used in either pour. There is no way to make a fresh panel match a weathered one on day one. What closes the gap is time and the same sun and traffic wearing on both.
Where the new joint ends up
A panel replacement gets saw cut back to the nearest control joint or edge, not just to the ends of the crack itself, so the new concrete meets the old at a line that was already planned into the slab rather than a rough break. That keeps the seam straight and predictable, even though it does not make it disappear. Where that new joint lands is worth asking about before the work starts, since it changes how much of the surrounding driveway or patio ends up a slightly different age.