Does cooking in a nonstick pan affect the finished food?

IMO, it's about firstly, temperature, and secondly, cooking time. Proposed solution is in the last paragraph. =-)

Explanation: non-stick pans (referring to the coated type), while being convenient, is not steel to oil, thus the oil is not heated at the required temperature consistently for the required length of time. This affects the crispness that you mentioned.

Take for example fried chicken, to get it "crispy on the outside, moist on the inside" requires a high enough temperature, and the oil needs to hold this high temperature somewhat consistently for long enough to cook the chicken. in non-stick pans, the temperature drops drastically as soon as you drop in the chicken pieces, and typically takes more time than one expects to get the temperature up again.

Solution: If non-stick pan is preferred, get one with a thick heavy base, preferably 2 layer designs. A deeper bowl design to hold more oil for the frying is preferable. Use medium heat to get the oil temperature up, before dropping the chicken pieces in. turn the heat up a notch after, for a short while to get the oil temperature up again, then turn it back down to medium again. experience will tell you what to do over time and practice. =-)

There are a lot of variables in getting food crispy, a non-stick pan being just one of them.

1. The type of food being cooked. A piece of onion will cook differently from a piece of meat or a patty covered breadcrumbs or batter etc. This is due to the moisture content of the food and also the Maillard reaction etc.
2. The type of oil or fat being used in the cooking process. Different oils and fats are more effective at crisping food, hence the use of duck fat to roast potatoes. I have found coconut or rapeseed oil to be better for crisping than cheaper vegetable oil, mainly due to their higher density and smoke point.
3. The temperature and cooking method employed. If you put cold oil in a pan, add food, then apply the heat, you will end up with oily, soggy food. Likewise, if you heat the oil to smoking and add the food, it will rapidly crisp up on the outside (but may not cook properly in the inside as the heat has not had time to penetrate).
4. Whether a lid was used or not during the cooking process. A lid will trap hot, moist steam and cause food to soften. Allowing steam to escape efficiently will improve crispiness.
5. As mentioned, the weight and materials used in the pan. My preferences in descending order are aluminium, anodised aluminium, steel and non-stick. The surface used has a lot of bearing on the quality and depth of the fond developed, the less "porous" the material, the less crispy. I can't really think of a better description than porous, as it is not smoothness as such (a mirror finish steel pan will result in crispy food, a smooth non-stick pan less so if you are trying to develop a fond rather than frying). By using an aluminium pan, you are allowing the food to initially stick to the bottom of the pan when added, and once a high enough temperature is reached, the food will come away with a crispy base. When using a non-stick pan, that "stickiness" will not occur, and the crispiness will be different.

Aluminum doesn't hold heat well. That's why it is used so often in the bottling and electronics industry - it simply wicks the heat away! Since the food is actually placed on the aluminum surface, the only place for the heat to transfer to is directly to the food. More heat per surface area equals more cooking to that particular area. Simple physics at work, and nothing more. Non-stick pans are typically steel based, and iron holds heat well (thus the deep, rich browning cast iron skillets are known for). Hope this answers your question.