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. =-)