Static methods are a lot faster and uses a lot less memory. There is this misconception that it's just a little faster. It's a little faster as long as you don't put it on loops. BTW, some loops look small but really aren't because the method call containing the loop is also another loop. You can tell the difference in code that performs rendering functions. A lot less memory is unfortunately true in many cases. An instance allows easy sharing of information with sister methods. A static method will ask for the information when he needs it.
But like in driving cars, speed brings responsibility. Static methods usually have more parameters than their instance counterpart. Because an instance would take care of caching shared variables, your instance methods will look prettier.
ShapeUtils.DrawCircle(stroke, pen, origin, radius);
ShapeUtils.DrawSquare(stroke, pen, x, y, width, length);
VS
ShapeUtils utils = new ShapeUtils(stroke,pen);
util.DrawCircle(origin,radius);
util.DrawSquare(x,y,width,length);
In this case, whenever the instance variables are used by all methods most of the time, instance methods are pretty worth it. Instances are NOT ABOUT STATE, it's about SHARING although COMMON STATE is a natural form of SHARING, they are NOT THE SAME. General rule of thumb is this: if the method is tightly coupled with other methods --- they love each other so much that they when one is called, the other needs to be called too and they probably share the same cup of water---, it should be made instance. To translate static methods into instance methods is not that hard. You only need to take the shared parameters and put them as instance variables. The other way around is harder.
Or you can make a proxy class that will bridge the static methods. While it may seem to be more inefficient in theory, practice tells a different story. This is because whenever you need to call a DrawSquare once (or in a loop), you go straight to the static method. But whenever you are gonna use it over and over along with DrawCircle, you are gonna use the instance proxy. An example is the System.IO classes FileInfo (instance) vs File (static).
Static Methods are testable. In fact, even more testable than instance once. Method GetSum(x,y) would be very testable to not just unit test but load test, integrated test and usage test. Instance methods are good for units tests but horrible for every other tests (which matters more than units tests BTW) that is why we get so many bugs these days. The thing that makes ALL Methods untestable are parameters that don't make sense like (Sender s, EventArgs e) or global state like DateTime.Now. In fact, static methods are so good at testability that you see less bugs in C code of a new Linux distro than your average OO programmer (he's full of s*** I know).
