The question of whether to BUY FIRST or SELL FIRST is a complex one. And a very personal one. There really is no right answer. The best answer is IT DEPENDS.
That may NOT what you want to hear, as someone who is relocating and needs to both sell your current home and buy one in your new location. I have been through it myself, on multiple occasions. So what issues should you consider?
1. Are you in a seller's market or a buyer's market? - talk with your agent, or you may already know. If you are in a seller's market chances are your home will sell quickly and at a good price (maybe full price or better), so buying another home before you sell is less risky. In a buyer's market the buyer is in control. So as a seller you are at the mercy of appropriate pricing, staging and condition of your home, and enough buyers who want your type of property at the asking (or near asking) price.
2. Your financial status - some sellers are financially in a position to be able to qualify to buy a new home (or pay cash) without having to sell. You need to look carefully at your situation to see if this can work, considering your market and the one you are moving into. You certainly don't want to have two mortgages if you don't need to (and especially if it is a financial burden).
3. Can you qualify for a bridge loan - if you need to buy before you sell, can you cover the costs of a loan to carry you through the process until your home sells. Many get into this situation after they have a signed purchase agreement but are waiting for closing. As a short time solution this can work well, but be aware bridge loans are pricey in terms of interest. You DON'T want to carry one for long if the closing time on your current home is lengthy, or worse, the deal falls apart.
4. Family circumstances - depending on the situation you are in with regard to your relocation, having your family settled in one place rather than living apart (kids, school, multiple jobs, etc.) may be a top priority. And it may be worth some extra money (with two mortgages) to buy something else before your current home has sold. But consider the issues above, too!
When trying to make the choice, I would also consider consulting your CPA on the tax issues, just in case there are some implications of your decision if transactions should overlap the tax year.
Keep in mind that as a seller in a buyer's market, you have no control. If you have bought another home but your current one is not selling, you don't have a lot of choice, other than to lower your price, carry the two mortgages, or rent your former home. Buying a new home AFTER selling is, for most, probably the most prudent decision. Proceed carefully.
Feel free to call me or send me an email if you have further questions. I would be happy to help you in any way I can.