If your old domain has been widely used and promoted, then presumably it has accrued back links, been mentioned elsewhere online, and will be recalled by people who have encountered it before. So there may be some residual value in those associations and even some inbound traffic.

Selling the domain would mean losing that. Since the domain itself may not attract much bidder interest and the sale price (if there is a sale) might be disappointingly low, you should consider whether it isn't better, after all, to maintain the current domain and have it forward automatically to the rebranded version of your website.