Just a run down:
Boys v. Girls
No getting around it, hockey is where the boys are, figure skating is where the girls are. I won't make a value judgment on that. If genderizing your kids is important to you (and I say that without sarcasm, as it is important to some), then I wouldn't even fight it. Put your boy in hockey skates and your girl in figure skates.
A lot of boys start in "regular" skates and then switch to hockey skates, but I don't see this happening in the other direction, and I should. Not everyone is cut out for team sports, and a boy who skates well shouldn't feel like he has to quit skating if he doesn't like hockey. Same goes for girls-- not all the little girls are graceful swans. We need to find ways to help kids feel good about switching to a sport they'll excel in, rather than sticking to the stereotype.
Just a caveat-- I'm not one to insist on rigid gender roles, but if you put your very young boy in white figure skates, or your girl in black ones (say under age 8 or 9), please give the coach other solid gender clues, especially if the child's name is "River" or "Tegan." Kids, especially in the 3 to 7 year old range, get really really annoyed when you get it wrong.
Skills v. Rules
Hockey and figure skating both have skills and rules. Hockey lessons tend to start with the rules and bring the skills in gradually, while figure skating starts with the skills and brings in the rulebook later. With hockey, I think it's largely a matter of ice availability-- you can learn figure skating rules at a desk, or not learn them at all if you never do testing or competitions, but hockey rules you have to learn while playing, and if the choice is game vs skills, game is going to win out in limited ice time.
But my observation is, except for the very talented kids, hockey players who took the time to build skating skills like stroking (striding), cross overs and turns before game time do much better at the sport. I am adamant that all skaters should learn basic skating skills before choosing whether to specialize in hockey or figure skating. In fact, I believe that programs should include required cross-discipline workshops so kids can find out whether they might like the other side better or not.
Easy v. Difficult
It is easier to learn to skate in regular skates, especially for very young children and timid adults. Period. The blade is longer and shallower, so you don't get the tipping over forwards and backwards. A beginner may trip on the toe pick, although this is much less common than the tipping over that you observe in a lot of beginners in hockey skates.
Expensive v. Cheap
Hockey is the more expensive skill to start. In fact, hockey clubs are perfectly brilliant. You require the parents to invest a couple/few hundred bucks in skates, padding, and equipment, plus a team fee, plus a uniform, and now you've got them, because they've just laid a bunch of cash on this and by god, that kid's gonna do this. I think figure skating schools should require skates, uniforms and memberships, too. Brilliant.
Seriously, though, the sense is that figure skating is this ridiculously expensive sport that will require a second mortgage, but upfront the cost is minimal. Even if you buy new skates, your costs the first couple of years are going to be way under what you'll sink into beginning hockey. At higher levels, most recreational youth sports will have comparable costs. And a hockey player with serious NHL aspirations, like a figure skater with a serious shot at Nationals, will spend some serious money on equipment, special coaching, traveling, etc.
Solo v. Team
There is team figure skating, called Synchro, but it is an advanced skill. Unlike hockey, you can't start with the team with minimal skating ability. Your little boy who isn't good at team sports at school, or likes to go off and play by himself, or with a couple of friends, or who likes doing his own thing, is not going to like hockey, no matter how much you think that penises confer a desire to play hockey. Conversely, little girls who join everything they can, who excel at soccer and t-ball and field hockey might be better off joining a hockey team than go solo.
I sometimes watch the hockey games, and observe the kids sitting on the bench rather than hanging on the boards, or hanging back on the ice doing artistic things with the sticks, or doing little jumps and spins and wonder, am I the only one seeing this? Put your artist in the artistic side of ice sports. Leave the hockey game to Killer (boy or girl).
Is your kid really into falling, crashing, bumping? Hockey. Figure skaters fall, just not on purpose, because no padding.
I've said it before lots of times. Ice is ice. Hockey skating will not keep your girl from wearing pink (there's a whole industry now of hockey equipment for the Princess in you. If Junior wants it too, you might want to rethink hockey). That said, figure skates will not make your son gay, if he's not getting there on his own anyway.