Would it be acceptable to tow a Honda Pilot instead of a Mazda 3?

I'm relocating next week, and I will need to tow either my car or my girlfriend's car behind the moving truck. I prefer to tow my car, leaving my girlfriend to drive hers that gets 35 mpg. However, when booking the truck and car carrier rental, I was told that none of their equipment fits my Honda which gets about 20 mpg.

I want to know if anything bad would happen if I towed my car instead of my girlfriend's smaller Mazda will this damage my car, damage the car carrier equipment, or have no negative effects at al?

Added (1). Spell correct: at all*

Added (2). Spell correct: at all*

Here's the thing, let's say you have to drive 1000 miles. 50 gallons for 20mpg and 29 gallons for 35mpg. Now that is 21 gallons difference or about 50 BUCKS extra. Now lets say you tow your Honda and it develops a problem, do you think the repair will only cost 50 BUCKS! This is called Penny wise and Pound foolish. To save a few bucks you may spend hundreds.

If your Honda Pilot is 4-wheel drive (or AWD), it should not be towed with two wheels on the ground so you can't use a tow dolly that only picks up two wheels. HOWEVER, U-Haul DOES rent auto transporter trailers that will get all four wheels off the ground and make it safe to tow your Honda.

Of course, the cost difference between renting a two-wheel dolly and a transporter trailer probably exceeds the $50 that Marduk mentioned, so you're really still not saving any money.

If either of the cars are automatic you can't flat tow them without catastrophic damage to the transmission. If either is a manual you can leave it in neutral and would be safe to tow.Anything further you would need to check your owners manual for specific towing instructions. But in general if the car is auto you either need to have drive wheels off the ground, or tailshaft and/or drive shafts removed.