Before I delve into which would be better for you, I should clarify something. The world of skis are not broken up into park skis and carvers. Most skis on the market these days are termed "all-mountain". This term can mean a lot of things, going all the way from something just a step away from a race-style carving ski, all the way to something that is nearly a powder ski, but toned down a bit. Some of them are twin tips. Some aren't. Some are light, some are heavy. Some are stiff, some are soft. There are a lot of options available to you, not just a park specific ski or a carving ski.
Second, its important for us to know where you're skiing. If you're skiing at a little hill in the Midwest, we're probably going to recommend a ski that performs better in hard snow. If you're skiing in Colorado, we'll probably recommend a wider, softer ski.
Finally, a park ski can still carve. Just because you are on a twin tip doesn't mean you would be unable to lay down an arc if you wanted to. To wit:
That's me on a pair of 99-underfoot, twin tipped park/all mountain skis. I'm skiing them arc-to-arc carved.
The hang up becomes when a park ski will carve. Ice? Not happening. Hardpack? If you're good, you can make it happen, but it's harder to do. Soft snow? Yup, you can arc a park ski in soft snow all day long.
On the flip side, you'll find a carving ski very poorly adapted to working in the park. A carving ski is going to make for difficult takeoffs, rough landings, and they're not going to like rails and boxes much at all. A well tuned carving ski's edge is going to catch on a box.
I'd lean toward an all-mountain type ski with a twin tip. Best bet for splitting the difference.