What are the pros and cons of RANSAC versus Hough Transform?
The Hough transform would be a reasonable approach for this.  Another reasonable approach would be to find connected regions of similar hue, and for each, test if it is approximately pool-ball-shaped.

RANSAC doesn't seem like a good tool for this purpose.  RANSAC is commonly used to find, e.g., a line that approximately  goes through a bunch of points (but possibly with a few outliers that might not fit the line).  Here, the pool balls are spheres, not lines.

RANSAC is typically used for other tasks: e.g., for aligning two images.  However, here image alignment probably isn't a good way to find pool balls on a pool table.