We are traveling with rental car across the English Channel and wonder about the shuttle (train) verses the ferry service, time and money differences?
Have you checked that your rental agency allows you to take your car across the Channel?
the ferry is cheaper usually, but both run all sorts of promotions and pricing is very much like airlines, ie every car in the line paid a different price.
the train is faster, but not if you actually want to be in Dover or north thereof
the ferry can be affected by weather at any time of year.
UK rentals will NOT be insured for use outside UK/Ireland unless you have paid a huge surcharge. French (and other mainland) might be insured for UK but the steering wheel will be on the wrong side. You need to be very clear whether prices include minimum 3rd party liablity insurance or full cover for the vehicle.
Years ago Hertz had a scheme whereby a Hertz car was driven to the Eurotunnel terminal and either switched to the opposite kind at the origination or destination terminal and then the driver just drove away. I think they called it LeSwap or some other naff marketing guff. It used to be advertised but I never saw a Hertz desk at either end.
Anyway, I think that that is now old history and I don't think the scheme exists any longer - but it might - who knows?
But for a normal rental I think that you may run into various difficulties.
If you can get it to work -
as mentioned above, my experiences suggest:-
The Eurotunnel is pretty much immune to French fisherman strikes and any French burning tyres tended to be nearer the Ferry Port - haven't seen either recently.
The Eurotunnel is immune to weather difficulties which can put paid to ferries.
The Eurotunnel is vulnerable to delays from migrants trying to walk to England or getting hit by trains - rare but it happens, and if there is a mechanical everything stops for a while because with only two train tubes there is no alternate route. I probably have delays about 10 or 20 percent of the time (I'm a regular traveler across the Channel and I never use the ferries anymore, ony the Eurotunnel) and about 20 or 30 percent of the time I can board an earlier departure for no cost.
The Eurotunnel tends to be more expensive, is much faster on my route, and is very frequent.