The Difference Between Bilateral Filter and Gaussian Filter
The Gaussian filter corresponds to isotropic diffusion (or the heat equation if you are familiar with it).
Its application to an image will blur it uniformly, whatever the image content, edges, etc.

The bilateral filter is almost like a Gaussian filter, except that the Gaussian is modulated by a function that computes the similarity between the central pixel (where the filter is applied) and a pixel in its neighborhood (that is used in blurring).


If the two pixel values are very close, it multiplies the Gaussian coefficient by something close to 1, and hence it is equivalent to Gaussian filtering.
If the pixel values are very different , it will multiply the Gaussian coefficient by a number close to 0, thus turning off the Gaussian filtering for this pixel.


Intuitively, this behaviour yields the following result: Gaussian filtering in uniform areas of the image, no filtering across object borders.
The bilateral filter will produce a more pleasant results, because it will avoid the introduction of blur between objects while still removing noise in uniform areas.