I don't think it would be worse to hit a deer; I'd rather take the impact higher up on the bike, rather than hit something with some mass that could actually make contact with the front wheel. Especially when you consider that, if the animal is massive and that low to the ground, like a hog, and you hit it with the front wheel, you're more likely to then run over it, rather than have it get deflected to one side or the other. That would be like running over a log. Even if you don't run over it, anything you hit that could forcefully deflect the wheel to one side or another at speed could be catastrophic and unrecoverable. Like Checkswrecks says, your wheels are like big gyroscopes when you're in motion; the faster you go, the more stable you are. If you upset the balance of one of those gyroscopes at a high speed, you've lost part of the force that's keeping you upright and stable.
I've seen a few videos from on board cameras on bikes where the rider hit a deer, and none of them resulted in a loss of control. One was on a Harley bagger (it might have been a Road King) and the other on a sport bike. On the Harley, there was barely even a wobble at the moment of impact; the handlebars didn't even move. Lots of damage to the fairing, headlight, etc, but after he hit it, he just did a nice slow controlled stop and pulled off the road. Maybe not that surprising on a thousand pound plus HD vs a 140 lb deer, but even on the sportbike the result was the same. As long as the deer doesn't actually hit you yourself, the impact doesn't necessarily mean you're going down. Unless the deer is leaping really high at the moment of impact, so that he clears the front of the bike and hits you, most of his mass is probably going to hit somewhere above the front wheel.
I'm not minimizing the danger of a deer collision; one big reason I avoid riding at night is because of them. But some of the crashes that result from deer impacts can be the result of just doing the wrong thing after impact.
And for our northern brothers who have to deal with moose.....yeesh! I didn't see a single one when I was up in Maine last year, but I was on high alert the entire time.