Selling first means you may need a flexible possession date, a short-term rental, or family arrangements for a few weeks between homes, which is an inconvenience rather than a financial risk. It also means you are shopping for your next home as a firm, qualified buyer rather than a hopeful one.
Buying first before Brighton sells adds carrying costs and the risk of feeling pressured to accept a lower offer just to close the timeline, which is exactly the scenario a downsizer with equity and no urgent deadline can usually avoid.
The decision changes if you have found a specific new home you cannot risk losing, in which case a bridge arrangement through your lawyer can work. Get your hand-reviewed valuation from Joel Dyck.