At one point I was told by a skate shop that sold both that most people who did both chose [quad] roller boots that were lighter and less stiff than their ice skates. Don't know if that is true. It must depend depend a lot on what types and levels of skating people are doing, not just on ice vs quad vs inline.
E.g., on ice, speed skates, hockey skates, and figure skates are a lot different, and there are different sub-categories within each of those. I tried a pair of ice blades for rugged outdoor use that clipped into XC ski boots, that was a lot different too, from skates designed for use on smooth rinks.
Some inline skates look almost like downhill ski boots, and are completely stiff and knee high, especially those used over rough terrain.
A lot of freestyle boots have low backs too, for comfort and extra toe point. E.g., Graf Edmonton Specials
http://www.grafskates.ch/skates/grafskates-kunstlauf/graf-top-level-skates/edmonton-special-v-insert/?L=1%C3%83%C6%92%C3%86%E2%80%99%C3%83%C2%A2%C3%A2%E2%80%9A%C2%AC%C3%8B%C5%93%C3%83%C6%92%C3%A2%E2%82%AC%C2%A0%C3%83%C2%A2%C3%A2%E2%80%9A%C2%AC%C3%A2%E2%80%9E%C2%A2are top level freestyle boots. But freestyle skaters need much more sideways reinforcement to keep the foot and especially the ankle within a safe range of motion. OTH, many ice dancers want full range of motion, especially at the ankle, though you still need some stiffness to give precise edge control and placement. Also, you can't get high level freestyle stiffness and durability without more weight. Ice dance boots are usually more comfortable, given equally good fit. But if you want to jump high, even a tiny little bit high like me, there is no substitute for the support given by freestyle boots.
I've never used "slalom" inlines. But I have Roller Blades, which are articulated. They are very stiff sideways, like high level freesetyle boots, almost like downhill ski boots. So if that is what you are used to... I think you would have trouble adapting inline slalom boots to figure blades, unless you are really good with tools. But I've never tried, though I've thought about it, because they are comfortably padded. Anyway, why should you care if people think your boots look funny? At least until you compete at upper levels, and have to worry about what the judges think. Haven't you watched the movie "Go Figure," where she starts out a figure competition in hockey boots?
For inline, certain PicSkate frames are often chosen by figure skaters, especially those with ice experience, and are a lot different from other inline frame sets, but I don't have the experience to talk about them. Maybe someone here can explain better.
But until you decide what type of skating you want to do, it will be very hard to get optimal boots and blades. Why not start with rentals, take a few lessons, try several disciplines, and decide then, with the advice of your coach and your best area skate tech? But I'm confused. I thought you already were doing freestyle? (Am I thinking of a similar name for someone else?)
As you must know, many would-be figure skaters start out on hockey equipment, or on freestyle or dance equipment, for the first few sets of lessons, regardless of what they eventually want to do. But it doesn't take long to get to the point where the right type of boots and blades makes a big difference. Nonetheless, you could take intro lessons in several categories.