What are the benefits or drawbacks of using a snooker cue rather than a standard cue on a regular pool table?
There's a few differences between a snooker cue and a pool one:
Weight: Because pool balls are heavier than their snooker cousins pool cues tend to be heavier to match. The weight distribution is also different - pool cues are heavier on the grip where snooker cues have more weight at the tip.
Tip size: Snooker cues have a narrower tip (~9-10mm vs 12-13mm)
So what do these differences mean? Snooker cues are optimized for accuracy rather than power or cue-ball control as pool cues are. This is the case because of various factors - snooker balls are smaller, the pockets are rounded (i.e. you have to be more accurate to pot then in pool), the table is significantly bigger which further increases the need for accuracy.
So to answer your question if you were to use a snooker cue on a regular pool table you'd benefit from potting accuracy but lose out on the ability to hit harder and to position the cue ball were you wanted. Additionally while the tip is only slightly smaller the difference in ball sizing means that using a snooker cue to hit pool balls increases your chances of miscuing and imparting unwanted spin on the cue ball (and ultimately object ball as well).