The pontoon boat's insurer isn't necessarily liable for your damage.
I can't give you formal legal advice because I'm not admitted to practice law in your State, but I can discuss a few issues from a general perspective that might come up in your claim. However, remember the laws in every State vary considerably, so advice from a local lawyer is best. (I'm not even sure what State your marina is in. If Louisiana, then I am particularly in the dark as that's the only State of the 50 that has French historical roots instead of the English common law rules the other 49 States follow.)
My comments are based on typical common law principles.
Maybe the pontoon boat's owner (and therefore insurer) is liable to you, and maybe it isn't. Your note doesn't provide enough facts to figure that out. In most States it isn't sufficient to say the other boat damaged you during a storm, and therefore it is liable to you. There has to be "fault", usually "negligence", which is typically defined as "failure to use ordinary care".
Why did the pontoon boat break free? If it was insufficiently secured because its owner only used one, small diameter, aged dockline per cleat, while everyone else in the marina doubled up, or used larger diameter lines, or stripped their boats of unnecessary windage, etc., then you might be able to prove fault and recover from the other guy.
On the other hand, if it was properly secured but was hit by a storm surge, a rogue wave, or winds so strong that even reasonably secured other boats broke free, then it's tougher to prove fault. More than likely there will only be a lot of speculation as no one actually witnessed the damage occur.
Many States don't assess liability if the damage was due to "Act of God". There are lots of cases where that's been raised and either accepted or rejected based on the specific facts of the incident.
If it's not too late, take lots of photos of not just your damage, but the rest of the marina, the methods used by others to successfully tie up, the lack of other boats that broke free (if that's true), the specific failings of this boat (undersized cleats, docklines, etc.) I'd concentrate most on the boats nearest the pontoon boat, as different areas of the marina may have been subjected to vastly different wind effects. Remember you're trying to show the other guy didn't use sufficient care in securing his boat, and the simple fact that he broke free or one other person didn't doesn't really prove much.
Fault issues normally don't matter to your insurer. If you have coverage for the loss, then they should owe you regardless of whether you or the pontoon boat or Act of God are responsible (unless one of those is specifically excluded by your policy or State law). Normally, though, you do have a deductible when the claim is against your carrier, and not against a third party's insurer. That's the biggest practical difference (aside from promptness of payment) in deciding whether to file with your carrier or make a claim against the other.
Your insurer can pay your claim, and if it thinks the loss was due to the pontoon boat's owner's negligence, then there are administrative or legal means for your carrier to get reimbursed from the other insurer if fault is proven. That's called "subrogation". As part of that claim, you would usually get all or part of your deductible also repaid if there's a recovery.
As you've probably figured out, the quickest way to get paid is to submit the claim to your own carrier. There isn't any need for a trial to prove fault if the other guy doesn't think he's at fault, or if his insurer just wants to be ornery.
One last issue for hurricanes. Here in Florida we now have sizeable "named-storm deductibles" that you may or may not be facing. The way these work is your usual $500 deductible on a claim is bumped up to let's say $5,000 if the damage occurred during a "named storm". Check your policy for details.