Waaaay too many variables to track here. Tires, pressure, gearing used, weight of each bike, position of body on each bike, etc, etc. Get a HR monitor, do both rides, report your findings back here. I'd bet though, that on neutral ground, at 10mph the difference will be on the order of (diddly/squat) squared.
Some heart rate monitors also have a built in calorie function. But I have a few monitors so I wanted to make sure that I use the same formula all of the time, as the different monitors use different proprietary formulae.
I think you will find that if the two bikes have the same tire pressure, that they both have very similar energy requirements. But different rider position and other factors will come into play. I for one would have a higher calorie ride if I was not as comfortable or if the bike geometry felt off, but that would be a geometry issue and not a tire diameter issue.