To the employer, is equity more or less expensive than payroll?

It depends.

On one hand, paying you in shares can be almost free for the company. The directors just have to pay for the administration costs of issuing you the shares. If they are paying you shares in lieu of a substantial amount of cash, this is like printing their own money.

On the other hand, the shares have some value in the market. Either:

• they need to buy existing shares off the market to transfer to you (costing about the same as paying you the money directly), or
• they issue you new shares but could have sold those same shares to the market ('almost free' to them, but there's an equal opportunity cost), or
• the shares might be worth a lot one day ('almost free' today, but the opportunity cost could be miniscule or it could be huge - think Bitcoin pizza).

The flip side is dilution. If the company had 10 shares, with 10 shareholders each holding 1 share, then each shareholder has 1/10 of the company. If they now issue you 1 share, there are now 11 shares, so the each of the original 10 shareholders now only holds 1/11 of the company. So long as your contribution grew the profits by 10%, that 1/11 with you (1/11 x 110%) is equivalent to 1/10 without you (1/10 x 100%).

So there's no easy way to say in general whether paying in shares instead of money is better for you or for the company.

Other than when they buy shares off the market and transfer them to you, the primary benefit of paying in shares is that the company doesn't need to give you the money's worth in cash. To get the money's worth in cash, you need to sell the shares. Since the company doesn't have to be the buyer, it can be someone else that foots the bill for the money's worth.

It's not a matter of cost, it's a matter of risk.

I created a startup. I expect that in one year's time its value will be zero or $1,000,000, but I don't know which. I want to hire you. Instead of a $50,000 salary, I offer 20% equity.

If you don't accept the offer, then one year from now I will have either -$50,000 or +$950,000. If you accept the offer, then one year from now I will have either $0 or $800,000. You could see that as a potential loss of $150,000, but I'd see it as either no painful debt, or still a shedload of money for me.

(For established companies, equity or share options are basically the same as creating new shares and selling the on the stock market, except possibly different tax treatment. )