The GND and a polarizer have very different uses, so the best way of deciding which to go assuming tight funds, is usage. I'll move this to accessories which will be a better home for it.
Used mostly for landscapes to correct balance between bright and dark areas, ie sky and land. Normally best as square filters so the position and angle of the graduation can be adjusted. Normally you get a set of different graduation strengths and hard or soft graduation.
Alternatives: Shoot using a tripod, take 2 or more shots at different exposures and combine in photoshop using layers (Sometimes it is enough to make two different conversions from a single RAW image): Advantages of this is more control over the effect, downside is more processing. Problems: Combining the two separate shots can be an issue if scenic elements are moving around the graduation line, ie trees in the wind, rapidly moving clouds.
Can be useful in a wide range of applications but the effect can be subtle. You must get a circular polarizer. A linear polarizer will mess-up the camera autofocus.
a) Increase colour saturation of the sky: Only effective at 90 degree angles from the sun, effect is a bit of a cliché.
b) Improve colour saturation of some objects. This works by reducing reflections off the surface of some objects (all reflection introduces a degree of polarisation). This can be very subtle to the point it is not really doing much for you.
c) Increase or reduce reflections in water and glass. This can be a strong effect.
Available for a square filter systems so you can use the same filter on all lenses (with a different adaptor). Also available as a traditional screw in round filter, normally with better quality coatings. The Hoya SHMC ones are very good and HMC pro 1 Digitals are OK. B+W MRC are also very good. Both B+W and Heliopan do more expensive hermetically sealed versions as well as the basic, these might be worth it for the tropics.
Alternatives: None. Can't be emulated in processing.
Disadvantages: I find I hardly ever use mine. Also typically cause a 2 stop light loss, not a problem if working from a tripod.