It's not surprising at all, and actually completely normal, that you had trouble with your transition from one skate to another. Here's why:
Figure skates and hockey skates are completely different styles of skates. Figure skate boots can have a higher heel which would put your foot at more of an incline than a hockey skate. Figure skate blades tend to be a little flatter than hockey skate blades. And of course there's that toe pick. Kids who start out on figure skates, then transition to hockey skates, can find it a little difficult at first, especially if they relied on the toe pick for balance, stopping, and acceleration. And vice versa, kids who start out on hockey skates, then transition to figure skates, can find themselves tripping over the toe pick.
You also mentioned your new skates were sharper. This could effect your ability to stop if you are used to having dull skates.
All it will take is time on the ice to get used to your new skates. Even going from an old figure skate to a new figure skate, or an old hockey skate to a new hockey skate, even if they are the same brand and model of boot takes a little time. Leather is stiffer on the new skate, the new boot hasn't conformed to the shape of your foot, and blades are at their original manufactured height as opposed to thinner due to being sharpened hundreds of times.
So just get out on the ice at a local rink regularly and you'll be used to your new skates in no time.
Also, if you want to speed the break in process a little for your new skates, you can try "baking" your skates (How do I bake my Bauer skates?How do I bake my Bauer skates?). This may help soften the leather a little and help the skate conform to the shape of your foot.