For calm lakes and ponds and slow moving streams a canoe has its advantages. Standing up to cast isn't unreasonable with some canoes in favorable conditions. Certainly there is opportunity to move around. Carrying gear is not an issue, just throw it in. Maybe you could even consider sharing your canoe with a bluefish, something unpleasant even to think about with a kayak. I haven't fished from my kayak yet, but I don't think it is well suited. The kayak has so little drag that fighting a fish will at least require developing some technique.
On the other hand any kayak will lower your center of gravity, be less affected by wind, and probably behave better in waves. A canoe on a windy lake with whitecaps can be a handful even if you are a good paddler. When I had my Pungo in these conditions it was easy to control and felt comfortable (my wife was able to handle the conditions too, but was less comfortable).
My canoes have been reasonably stable general purpose boats. When pushed too far they would suddenly flip. The Pungo wouldn't flip, it just took water into the cockpit until it became unstable. It took some effort to make this happen.
The Pungo behaves well in fast moving tidal creeks and is far superior to a canoe in terms of paddling ease in this environment. The double bladed paddle probably helps less experienced paddlers keep the boat under control, but I guess you could paddle a canoe with one too.
If you can flip a canoe up on to your shoulders it really isn't a chore to carry it (single handed) a couple hundred yards if the wind isn't a problem and you aren't sharing the inside of the canoe with hundreds of biting insects. Despite the lower weight of the kayaks, they don't seem easier to carry. Two people can easily carry two kayaks however by grabbing the handles on the ends.
I can roll a kayak, but rolling a Pungo even with a skirt would be just a stunt. They are designed to allow you to get out (read fall out) easily under any condition. In contrast, a whitewater kayak "locks you in" with thigh braces and footbraces. If you don't roll, you have to get yourself out of the kayak. I did take my whitewater kayak out into moderate post storm waves years ago. In this boat I was comfortable having the whole boat underwater occasionally under whitewater conditions. Powerful ocean waves are another thing. The combination of undertow, rip currents, and waves that could pound you into the bottom are best avoided, IMHO. It is possible to empty a swamped Pungo and get in it in chest deep (calm) water, but I didn't experiment in deeper water. Don't expect to be able to do so without a little practice.
The Pungo's tradeoffs are great for getting from point A to B or just cruising around in bays and salt creeks in my opinion. My wife is delighted with hers too and, although she has paddled a canoe with me, she had no kayak experience. But, don't sell the canoe, it has its place.