Is there a general rule as if should bake something at 375 or 350 degrees, or does it really matter?
Experimentation is the key in any recipe development, informed by the effect of the variable under investigation. 

In baking cookies, the affect of the oven temperature will effect:


Spread.   Cooler temperatures will allow the cookie to take longer to set, and so it will have longer to spread before it sets.
Height.  This is the compliment to spread; cooler temperatures will allow the cookie to spread more, so it will have less height.
Drying.  Cooler temperatures will allow the cookie longer to express steam, providing a somewhat dryer cookie.  At its extreme, you can make quite dry, wafer type cookies.
Evenness of cooking.  Cooler temperatures cook allow the to cook more eveningly from the outside to the inside.   Hotter temperatures may allow, for example, browning at the edge or surface while the interior is under-cooked.


In most cookie recipes, the difference between 350 and 375 F may actually be smaller than other uncontrolled variables like the type of oven, individual oven variance, type of cookie sheet, size of individual cookies, and so.   Additionally, within certain limits, there is a trade off between time and temperature.

For these reasons, you will need a high degree of consistency if you are doing dry runs to try  to determine the optimal temperature.