Most tree frogs are strictly nocturnal, so they only come alive when the lights go out. If you've been watching him in the daytime, all you'll see is a green lump. But White's move around quite a bit at night (at least mine did). So yes, vertical space would certainly be appreciated. If you really don't have enough for the bigger exoterra, there are other options. You could get a vertical conversion for your 10 gallon, either getting the parts from a hardware store or purchasing a kit. You can also pick up a larger tank, say a 20 gallon high (I've had a lot of luck with craigslist), and doing a vertical conversion on it.

No I don't think he'll get lonely =) But rather what I meant was, if you decide to get him a friend later on, the bigger exoterra tank will be able to support two adult White's comfortably.