Three paths, three very different trades
Franchising means selling other people the right to run a location under your brand and system, in exchange for a franchise fee and ongoing royalties. You keep the brand and a recurring income stream, but you take on the FTC Franchise Rule's legal obligations, and your income now depends on how well franchisees execute — people you don't manage as employees.
Selling to a private-equity roll-up means selling your business outright to a platform that's acquiring similar shops and combining them into a larger company (see Sell to Private Equity in the Exit & M&A track). You get paid — commonly a mix of cash at close, an earnout, and rollover equity — but you give up the brand and, usually, day-to-day control. This is an exit, not a growth strategy: it's the right comparison when the real question is "should I sell" rather than "should I expand."
Licensing your brand or process is the lightest-weight option — you license your name, methods, or proprietary systems to other operators without the full franchise-law machinery (the FDD, state registration, ongoing franchisor obligations). It gives you less control and typically thinner royalty economics than franchising, but far lower legal setup cost and complexity. It's a reasonable middle path when you want some brand leverage without committing to being a franchisor.
How to actually choose
If you want to cash out and step back, a roll-up sale is the right lane — read the Exit & M&A track, not this one. If you want to keep the brand and build recurring income and are willing to take on real legal/operational complexity, franchising is the fit — start with should you franchise your business?. If you want to test brand leverage cheaply before committing to either, licensing is the low-cost way to find out whether your name and system travel at all.