Which works better, Prilosec or Nexium?

Laurent is right that they are the same TYPE of drug, but they are different chemicals (meaning different drugs). http://www.drugs.com/pdr/prilosec.html points out that generic Prilosec is Omeprazole and http://www.drugs.com/nexium.html points out that generic Nexium is Esomeprazole. They have the same effect (helping to prevent your stomach from producing enough acid), but they are different chemicals.
The answer to your question unfortunately depends on your system as far as how well your system responds to the drug. You could start out with the cheaper one and see if it works well enough for your needs.

I also wanted to point out that both of those websites list that it is prescribed for typically 4-8 weeks and really shouldn’t be taken longer than that because they prevent stomach acid from being produced. The reason that can be so bad is that you obviously need stomach acid to break down your food so you might not be absorbing all the nutrients you need from your food if you take it too long, which would literally starve your body of certain nutrients over time.

If you would like some healthier and/or natural options, there are some herbs that help to neutralize stomach acid and help with the overall issues like that. For home remedies, baking soda in water is the best and quickest option that most everyone will have, but I would also avoid spicy and highly acidic foods (citrus and whatnot) as well until you feels better.
If you’ve got Apple Cider Vinegar, I have heard of many people curing their reflux by taking that on a regular basis to help normalize the acidity in their stomach, but that’s not as much of a “quick relief”.
Good luck and I hope I helped!

Personal experience and personal research in my role as a Product Specialist for a vitamin company