The canoe Vs kayak debate is full of apples to oranges comparisons. People compare Lightweight 55 pound 14 foot kayaks to the 16 foot heavy duty canoes that they paddled in summer camp as a 75 pound kid. As a result there is a huge amount of misinformation out there. 14 foot Solo kayaks should be compared to 14 foot solo canoes. 16 foot tandem kayaks should be compared to 16 foot tandem canoes. Hopefully this will help you sort through it all.
Keep in mind that being able to take advantage of a benefit of one over the other often requires considerable skill.

There are 3 primary diferences between canoeing and kayaking.

The most obvious is that kayaks have a deck while canoes are open.
In open water, like sea kayaking, and in white water, class 3 and above, the deck of a kayak is a substantial advantage. When combined with a spray skirt the seaworthiness of a kayak can't be beat. A canoe with airbags can come close, but not equal a kayak when the waves get big.
The deck also allows a lower profile for better performance in a crosswind.
The downside is that these advantages are dependant on the spray skirt and safe use of the spray skirt is dependant on the ability to Eskimo-roll.
Without the sprayskirt, the advantage of the deck is minimal.
Sure, you can pull the release and bail out. It's rare that you need to bail out on still water, so you can assume that you are bailing out into moving white water with rocks and strong currents or moving brown water with hidden stumps and quirky currents. Do you really want to be taking an unplanned swim with the mini-parachute of a sprayskirt around your waist to drag you under or snag on some hidden hazard?
Without the ability to Eskimo-roll, the spray skirt is a safety hazard rather than an advantage. Without the sprayskirt a kayak is craft for calm water and easy rivers.

The second most obvious difference is that canoes are most often paddled with a single bladed paddle, kayaks with a double bladded paddle.
Because a kayaker generally sits lower than a canoeist the double bladed paddle is almost mandatory. Sitting low, just above the waterline, dosen't allow the proper body mechanics to use a single bladed paddle comfortably or effeciently.
One advantage of the double bladed paddle is that the learning curve is short. Almost anyone, no matter how klutzy, can paddle in a straight line.If you make the same mistakes on the right side that you make on the left side, you still go straight.
Another advantage is that there is less time between strokes so a canoe or kayak can be paddled just a bit closer to maximum hull speed with a double than with a single bladed paddle. That's why kayaks are generally faster over a short to medium flatwater run than canoes of similar proportions.
A big disadvantage is that there is less time between strokes so that your muscles have less time between strokes to rest. That is why canoes catch up to kayaks on medium length flatwater runs.
A bigger disadvantage is that the paddle strokes are farther out from the hull than the strokes of a single bladed paddle. This causes a slight zig-zag on the course of your canoe or kayak. Each small change in direction wastes energy in the form of turbulence. This can be reduced, but not eliminated, by designing a hull with less rocker. That's why most kayaks have less rocker than a similarly sized canoe designed for the same job. Rocker, the front to back curvature of the hull, is important for manuverability. That is why a canoe will out turn a similarly sized kayak. It's also why a skilled canoeist can easily outrun a similarly sized kayak on narrow winding rivers like those in the NJ Pine Barrens.
A single bladed paddle is used close in to the hull. This minimizes the zig-zag although it does require directional correction during each stroke or frequent switching sides. Either way, less energy is lost to turbulence from zig-zaging than with a double. Paddling 14 inches out from the centerline of the hull causes less turning force than paddling 24 inches out from the centerline. It's simple physics. Less energy wasted means more efficiency. That's why canoes slightly outrun kayaks of similar dimensions over long flatwater runs.

The third most obvious difference is seat height.
Seat height affects body mechanics. Using a single bladed paddle pretty much requires a higher seat than is found in a kayak. The near vertical, close in against the hull, placement of the single paddle results in a better "bite" on the water as well as better arm position for the paddler and the ability to use back muscles in conjunction with a straighter arm position for propulsion. By spreading out the effort over more muscle groups fatigue is reduced.
The top grip of a single paddle allows more precise control of the rotational position of the paddle. The human brain and body is capable of incredible precision with the proper feedback and the mechanical advantage to be able to use fine motor skills. Precision is key to the more advanced paddle strokes, the strokes that allow a degree of control that allows finesse to replace force.
One of the advantages of a higher seat and a single bladed paddle is better control on gusty winds. The ability to paddle only on the upwind side, using tension strokes, gives a distinct advantage to the canoeist.

These advantages and disadvantages interact differently on different water conditions and with different skills.
For paddling open water and class 3 white water sea and white water kayaks rule the waves.
For beginners that plan on paddling ponds, small lakes and never want to do anything adventurous or take the time to learn any advanced skills, general recreation kayaks are the way to go. The fact that this is the biggest market segment of the paddling market says a lot about todays society.
For people that want an ongoing learning experience and the reward of more fun for far less effort, buy a canoe.
For people that want to go on multi-day trips with more than the bare minimum amenities, even a small solo canoe will carry far more than a kayak.
For the safety conscious, the increase in control of using a single paddle over a double, the ability to wear a higher flotation PFD with comfort and the far less likelyhood of an entrapment all are reasons to go with the canoe. Our experiences over the years clearly show that the risks are higher in kayaks and when paddling canoes with double paddles.
For ease of cartopping, the canoe fits on a flat rack while the kayak needs special bracket set.
For light weight, go with the canoe. A good 14 ft solo canoe weighs 40 pounds compared to a kayaks 55 pounds. The difference is less with a tandems, but a tandem canoe is still lighter than a tandem kayak.

We do no sea kayaking at all and rarely get into whitewater over class 2. We do lots of tight winding little rivers and about half our trips are overnight canoe-camping trips. So, if you plan to paddle with us on any of our more difficult trips, get a canoe. A few trips are kayak friendly, but not many.