Towing with a Honda

Given the choice, I'd pick the Pilot over the Oydessy. Better clearance and driver seat height, better frame for towing, amongst other advantages.

Tow ratings are not just based on horsepower. A lot of people get confused by that. There is a lot more to towing than "grunt". Wheelbase, frame design and structure, brake swept area, final drive gearing, etc. all are considered when the manufacturer comes up with it's rating.

If it was just about power, a Dodge Viper would be the ideal tow vehicle.. but most would recognize right off it isn't..

I used my 2005 Pilot to tow my 3400 lb Travel Trailer and it worked fine. I finally traded the Pilot in because I felt that I was stressing about my trailer weight  (i.e., not carrying any water) more than stressing about where I was going to fish. I error on the conservative side and subtract 2% of my tow capacity for every 1000 ft of elevation gain. That was limiting the passes in Colorado I could use. I tried to keep it under 10,000 ft. At 10,000 ft that is 20% or 700 lbs of lost towing capacity. Even if you figure that the pass is only a small amount of your trip so you take off 1% per 1,000 ft that is still 350 lbs. I guess what I am saying, if you want to travel everywhere, do not cut the tow capacity to close. I traded in my Pilot for a Tundra Pickup. With the towing package it is rated for 10,400 lbs. and it cruises up the Colorado passes.

Another note on the Odyssey, The hitch height is very low compared to the Pilot. My friends with an Odyssey tow a four canoe trailer and it will scrap the hitch on some driveways. And that trailer is only 400 to 600 lbs.

The Pathfinder sounds like a good choice...not too big, but plenty capable.

Welcome.  Locking out OD is usually necessary when towing.  Things I've done to improve fuel consumption include low-rolling-resistance tires and synthetic oil.  I've been experimenting with higher octane fuel on the trip I'm on right now, even though it isn't required in my TV.