Local Services Ads sit above everything, carry the Google Guaranteed badge, and charge per lead rather than per click. You get verified, you get the badge, and disputed leads can be credited back.
Search ads sit below LSAs and above the map, charge per click, and give you far more control — exact wording, exact suburbs, exact hours. That control is where budgets are won and lost.
Neither is a set-and-forget channel. The money leaks through irrelevant search terms, ads running when nobody answers, and calls nobody tagged. Weekly maintenance is most of the job.