If the old portion of cement has no cut in expansion joints, it would be a good idea to begin cutting in new ones (cement saw @ 1/2 the distance of floor depth, thoroughly vac, clean sidewalls with denatured alcohol, then fill in with resinous grout material with properties of elongation @ 200-300%). This is applicable for the cracks that can be filled from top to bottom accordingly. Smaller cracks can be addressed with smoother flowing resinous modified materials.
Specialized fillers should never be applied unless the cause for failure is addressed properly.
Every crack in older floors has had dirt and grime seep up and down the inner sidewalls already…hence; it is a good idea to make sure that the contractor cup grinds every crack as mentioned earlier, with (high rpm equipment) then…. Blow out remaining particles and brush in acidic liquids at percents that will easily remove excess grime, nor cause further damage to your concrete by balancing the pH level afterwards. Thoroughly dry out each crack after this process… Fans, heat and low humidity levels are a blessing for proper drying at this point.
“Properly” for the old concrete will involve oil removal (Mechanical etching/Wet-Vac P/U of oily sediments – PH balancing - then let thoroughly dry) before shot blasting that area to a 60-80-grit feel and blow out the remaining dust that wasn’t picked up by the simultaneous Blast and Vac process…
This of course applies to garage flooring poured and cured w/o any expansion joints cut or troweled in the first place.
I agree with the last statement on the possibility of heavy movement from settlement...
So, make sure those areas are ground down effectively for "leveling" to save on overlayment materials...
It can be done to perfection!!!