Which one is better after a lot of vomiting: ginger ale, or gatorade?

Both: Ginger has some benefit in reducing nausea. Gatorade will help with dehydration and can also help reduce diarrhea (should that occur) as it contains the simple sugar glucose rather than the more complex sugar sucrose.

Of the two, Gatorade: When you vomit, your body loses lots of fluids as well as electrolytes like sodium and potassium. Gatorade can replace the water lost as well as some of the electrolytes, but has much more sugar than necessary. Ginger can be soothing to stomachs, but the carbonation in the soda may cause a recurrence of nausea. Pedialyte is probably better than either (but doesn't taste as good).

Ginger ale vs gatora: Ginger ale may be more helpful in helping stop vomiting - ginger has been used as a medicinal herb to stop vomiting. However vomiting can cause electrolyte imbalances which the gatorade may help resolve. So - gatorade in my opinion is better.