There are two parts to this question, the stated part, and the unstated "are you really frying an egg if there is no oil?"
For the first part, most manufacturers of non-stick pans claim that their product makes oil unnecessary, and generally I've found that to be true. A little oil helps, but "necessary" might be a stretch.
To maximize your non-stickyness of a non-stick pan, you should always preheat the pan before adding the food, at least to 250F or so. Preheating causes the teflon to expand a bit, closing up pores and micro-scratches in the surface.
It is also common for oils from the past to form a polymerized layer on top of the teflon, making the pan more sticky. This is actually worse when you use aerosol spray oils, because the tiny droplets hit the pan and very quickly polymerize to form a slightly sticky layer. This layer is similar to the one you intentionally create when seasoning a cast iron pan, but in this case it is not helpful. All-Clad recommends periodically cleaning teflon pans with a light scrub of baking soda and water to remove that coating of oil. It should bring back the maximum slippery of your teflon.
When cooking protein-rich foods, you can also minimize sticking by letting the food cook a bit before attempting to move it. The loose, floppy denatured proteins in an egg are extremely sticky, but when they coagulate (set) from cooking, they become less sticky. It may seem impossibly sticky at first, but may release on it's own after a minute of cooking.
As to the second, unstated part, oil provides flavor, and is also a heat-transfer vehicle. When the food is on the pan, if you looked at it with a microscope only a small portion of the food is actually in contact with the pan. Those areas will get heated more, and other areas will get heated less. A little oil fills those gaps, causing more even thermal contact, which allows fried food to fry, rather than just get burned in some areas.
It is really a matter of taste whether the flavor of the oil and the way that it changes the texture of the food is appealing to your boyfriend. I wouldn't like it without any oil, but if he does, well, so be it. If he doesn't really like the taste, but is concerned about health, I'd suggest using a little olive oil - it has no cholesterol, is low in saturated fats, and has a good flavor. Different than butter, but still very enjoyable.
America's Test Kitchen says that good quality nonstick pans last them about six months.
They're presumably cooking with them several times a day, so if you use it once every couple days, and are as good as they are about not doing things that'll damage the coating, you might get a few years. So your experience sounds roughly normal.
As another data point, they also quote the Cookware Manufacturers Association: "'If you get a year to a year and a half of life out of [a new nonstick pan], we think you got a pretty good deal.'" That's coming from people interested in selling pans, possibly not talking about the best quality, and with experience based on typical less-careful usage, so I'm not surprised they gave a lower number.
Best Answer
The theories that have come out in comments are most likely right on. Cast iron is special in how well it retains heat. Give cast iron ample preheating time, and you can drop in cold food without a significant drop in the temperature of the pan. That equals crispy. Even a pretty good and heavy non-stick pan is not going to give sweet potatoes the kind of crisp you can achieve with cast iron.
You mention higher sides in the non-stick pan. That alone probably wouldn't make much of a difference, but considering that you're already seeing a greater drop in temperature as you put in the potatoes, the higher sides would hold in more moisture in the cooler pan. That is not a friend of crispiness.
You say that you preheated both pans to about the same temperature. I actually hope your memory is a little off on that :) One of the great joys of cooking with cast iron is that you can and usually should pre-heat it to a quite high temperature without damaging the pan. Teflon, on the other hand, should never be preheated beyond a very moderate temperature for a very short time. Some people go so far as to say that you shouldn't preheat it all. So if your beginning temperatures were about the same in the pans, they shouldn't have been. After you put in the potatoes, forget about it. You'll never get the same kind of crispy sear with a teflon pan as you will with cast iron, even if you don't know how to best exploit the advantages of cast iron.