It seems as though there are different coverages and "clauses" between the different agencies. I compared prices a few years back and found little price difference for the same coverage. I heard "horror stories" about coverage "gaps" that were scary… but it is always hard to tell how much is true. I checked after each "story", and found no issues with my policy (Condon-Skelly for 27 years). There a at least a few other highly-recommended sources, too.
Insurance [to me] is very complex, I would recommend going with a company that has a good reputation among people that you trust.
For the "flatbed towing", "AAA Plus" covers daily drivers and collector cars (I think up to 100 miles).
Good luck.

2/25 – noted that the Condon-Skelly brochure "We insure your fun" has a picture of a Sunbeam on the front.