Hairline cracks are normal. Concrete shrinks as it cures, and control joints are there to guide that cracking into straight, planned lines. A few thin cracks that aren't widening or shifting are usually cosmetic and can be sealed.
Replacement becomes the better option when sections have sunk or heaved, creating a trip edge, when cracks are wide enough to fit a coin and keep growing, or when the surface is flaking and crumbling over large areas.
The cause is almost always underneath. Water running under the slab, a base that was never compacted, or tree roots lifting a section won't be fixed by patching the top. The new patch cracks along the same line within a season or two.
Replacing a sidewalk or driveway section means breaking out the damaged concrete, hauling it away, correcting the base and drainage, and pouring new concrete doweled into the good sections so they stay level with each other.
If you're not sure which you need, we'll look at it during a free on-site estimate and tell you honestly whether a repair will hold or whether replacement is the better use of your money.