How to decide whether to make a claim with homeowners insurance or the at-fault driver’s insurance?

Context: I live next to a business. That business hired a landscaping company. The landscaping company “parked” their truck and trailer then walked away to begin their job. Somehow, someway (landscaping company is claiming the truck has a historical issue of slipping gears) the truck traveled about 50-60 feet and collided with my detached garage, significantly damaging the concrete foundation and the brick wall and caused the garage door not to function properly. There is video footage of the collision from the business next to our house and a dash cam in the landscaping truck. The police were called and there is an incident number recorded.

We’ve been advised of the 2 options for getting it covered (our homeowners vs their commercial auto) and understand some pros and cons, but there doesn’t seem to be a clear choice. Our homeowners insurance includes $67,000 coverage for other structures with a $1,000 deductible, but the customer service rep danced around whether premiums would go up and the impact that subrogation could or could not have on the claim if we chose to file it with them. We haven’t yet contacted the landscaping companies insurer. Just hoping to get any advice and input. Thank you!