Why do people say that convertible debt financing is cheaper and/or quicker?

The biggest sticking point in any private investment tends to be valuation and share % ownership. With convertible debt, the valuation is kicked down the road to a priced round. The problem with debt is that it ranks higher than shareholders and so is not true risk-sharing, especially if directors/founders are asked for personal guarantee. There are some that argue that uncapped convertible debt doesn't align the interest of investors and founders (see http://techcrunch.com/2012/09/05/why-convertible-notes-are-sometimes-terrible-for-startups/) . Hence seed financing have standardised on financing for future equity documents. As for the choice for angels, follow the golden rule ... he who has the gold makes the rules.