I don't see a lot of difference between drinking few sips and 1 cup (8 oz, 237 mL) of water at once.
If you drink a large amount of water at once, for example, 500 mL (2 cups, 16 oz), all this water will be quickly absorbed and will expand the blood volume. Volume receptors in the heart will detect an increase of blood volume and will trigger excretion of some water from the blood through the kidneys before the water could reach the body cells. This way the drinking will be less efficient than drinking smaller amounts, like 1 cup at the time.
This can be true even when you are dehydrated and you, for example, miss 2 liters of water in your body (you can know that by weighing yourself). When you drink 1 liter of water at once (still only the half of the amount you miss) you may observe that you will need to urinate shortly after that (because of mechanism described above). If you drink smaller amounts, like 1 cup (237 mL) at the time, for example, 30 min apart, you have a better chance to keep a greater percent of water in your body.
Water intoxication is not studied by experiments, from obvious reasons, so the most knowledge about this comes from case reports and newspaper news.
According to one report, a woman who was on a low-calorie and hence low-sodium diet for about a week, drank 4 liters of water in 2 hours and later died in hospital from water intoxication (hyponatremia).
This is the lowest amount to cause water intoxication in adults, I've heard of.
One US military source recommends drinking only up to 1.4 liters of water per hour, when you drink it for several hours in a row.
More cases of water intoxication: