I have an older less valuable model but it has to the second type for me as it's the only way to get European breakdown cover. Most breakdown insurers won't touch you if your car's over 15 years old.
I haven't found that to be the case.
I have several cars insured with Classicline and European breakdown and recovery is included as standard in their policy.
They're very competitive in my experience and also insure "modern classics"