This is a common question that people have making the decsion to move. There is no clear answer, a lot depends on your own personal situation and risk tolerance.
Selling first puts you in a stronger postion when making your purchase as you do not have a house to sell, and sellers like that. It means less conditions to your purchase. But it does have some risk in that will there be the right house for you available, can you find it and close on it before you have to vacate your existing home. Do you have another place you can move to in the interim if the possession dates do not align?. Lots of emotional stress with this method, as there is a risk of having to make a double move. But the advantage is that you know exactly what you can afford, and your subsequent offer on the next home will be a stronger one as you already have yours sold.
If you want to purchase first then sell your existing home you will in all likely hood include a clause that will make your purchase "subject to the firm sale of your existing home." We do this all the time, however the downside to this is that sellers tend to want close to their asking price, and they will most likely include a counter clause that says they will continue to actively market their home. What this means is that If they get another offer they like, they can accept it subject to the existing offer between you and the seller collapsing. The seller will advise you of the second offer and you usually have a predetermined amount of time to clear all your conditions, including the sale of your exiting home. If your home has not sold or your can't waive all your conditions then you will have to collapse your deal with the seller, get your deposit returned and start looking again. Lots of emotional pressure on this one as every day that your home is on the market is another day you could lose the one you have already chosen.
There is a third option that falls kind of between the forgoing two. It involves actively looking at the homes currently on the market first. If you can say to yourself after seeing a few that if you had the cash you would be comfortable in putting an offer on any one of several, then you will have that comfort level that there will be a suitable home for you when you get yours sold. Now we go to market with yours. While your place is on the market we continue to stay on top of what is available for your purchase. That way when an offer is written on your place, you can make your sell decsion based on the knowledge that there are some good choices for you currently available.
As I mentioned before, there is no clear cut answer. It is very dependant on your financial situation, your tolerance to risk, the emotional side, and what your needs are in the next home. Lots of decisions to be made.
Hope this helps in some fashion, and you can certainly call me if you want clarification on any point.