We just launched our startup with a designer helping us pro bono to spruce up the design of it. He's asking for compensation now (which is fair) and is willing to trade in his service for equity. Just wondering if it's better to pay than to trade equity for the service.
William explained the basics of the problem, so it's really up to you.
It's a matter of risk and initial investment. If you believe that your startup is a winner (which is logical, otherwise why spend time on it?), then you'll probably expect it to grow to a $1M/$10M company. You can calculate the equity then, or the rough amount of work based on time spent * hourly rate.
The other part is the risk. If you're wrong, equity will cost you less. If you rely on a loan/mortgage, this could pay back later or you'll be debt-dependent later on. It's a matter of calculations, risk, planning and connections.