Yet upon closer inspection they revealed some interesting differences:
I like this because, to me, it doesn't reveal the stupidity of the signmaker. It reveals the stupidity of the system. What IS the best way to handle issues of agreement in these signs?
In the first one, at vehicle owner's expense is a fine choice. But it ignores a flaw. It attributes to multiple vehicles a single owner.
The sign with the sticker appears to be a noble attempt to fix this. To correspond with multiple vehicles, it references multiple owners. You've got to applaud that effort.
But vehicles owners doesn't work. The plural of vehicle owner doesn't include an S after vehicle. You could use vehicles, but it only makes sense as a possessive: vehicles' owners'. And that's just weird.
The only way to get around this agreement problem without creating weird possessive issues is to write:
All unauthorized vehicles will be towed at the expense of their respective owners.
But that defies another priority for signmakers: economy of words.
So with that, I'll just express my sympathies for the people who have to make these signs and, out of respect, will refrain from mentioning the issue of capitalization.