When negotiating offers for non-public companies I provide a sliding scale of cash vs equity. 1 dollar of cash is worth to me 10 dollars in equity of a private company. So if my total comp goal is 300k per year you can give me 250k of cash and 500k of equity, 200k cash and 1000k equity, or just 300k cash.
Most companies will baulk at this, but in my experience you have none of the power when holding private equity and so you need a really large multiplier to make it worth the risk.
Equity in a public company is a totally different story because the company valuation is controlled by the stock exchanges and you can cash out you equity at any time.