Thanks, Diane, for the question! I use both in my business, here are the pros and cons of each to help you decide:
Oil based polyurethane gives a warm, golden glow to your wood floors. This is a very traditional look that compliments other rooms in your house that may also have an oil-based polyurethane on the wood floor. Oil does, however, smell very strong- it is not as environmentally friendly because it has higher VOCs (volatile organic compounds) than water-based. It also takes quite a long time to dry between coats, so plan on being out of your house (or at least not using the room or rooms) for a few days. Floors typically require at least 3 coats - a coat of oil based sealer and then two coats of what most consider the "finish" - the oil-based polyurethane. Between the sealer and the first coat of finish, you need 24 hours. Between the first coat of finish and the second coat, you need 36 hours and then after the last coat is applied, you need another 36 hours. Oil based sealer and polyurethane are less expensive as the product is actually less expensive and it is easier to work with for the novice. You can work it when it is still wet, and you don't have to work quite as fast. The warm glow also covers up quite a few technique flaws.
Water-based on the other hand, although milky in the can goes on clear. It lets the natural color of the wood show through and is ideal if you do not want a golden tinge to your floors, which complements a variety of floor wood choices and keeps stain colors more accurate. Water based sealer and polyurethane have less VOCs, which is most people and research considers safer and healthier. Water based does take less time to dry between coats- typically only 2-3 hours depending on the weather, so the overall time frame of the job is much less. You also don't have a strong smell permeating your house, so simply not using the room being refinished is an option. The downside of water-based is that you definitely need to know how to work with the product- it is clear, so it can't hide technique flaws and it also dries very quickly, so mistakes can't be smoothed out as you work along. The product is also much more expensive than oil-based. If done right, in my experience, and if using the higher end water-based products currently available, it lasts just as long as oil-based finish. My current top choice is called Bona Traffic and you can read about the product here. I highly recommend getting a contractor experienced with water-based polyurethane in to do this type of job and not tackling your first flooring refinish project on your own using water-based polyurethane.