You don't have to over-complicate the analysis. The fact that they give you the options instead of cash is proof the options are worth less than the cash. This is Econ 101: bad currency drives out good as good currency gets horded.
Secondly, options incentivise people to stay around (until their options vest). The company also gets to cancel unvested options if a person leaves and even claw back vested but unexercised options in the case of misconduct by the employee. These are all things that are valuable for the company and more difficult to achieve using cash.
Thirdly, there is a big difference to most startups between "value" and "cash". I may well want to pay someone in a cash-equivalent that has equal value to cash (or even greater) because I want to manage my cashflow. After all, I can pay my employees (some of their comp) in options but I have to pay my bills in actual cash, which may be hard to come by until I hit net positive cashflow. In the case of an option, when you exercise and sell, you turn your option into cash, but the cash doesn't come from the company, it comes from whoever buys. This may be more efficient for the company than raising the equivalent cash and paying people directly in cash (because of transaction costs around fundraising).