It's mostly a function of how the transistors are made. If a transistor is on by default, they're called "depletion-mode" transistors--this means that the channel between the two sides of the transistors normally conducts, and via the control voltage, you deplete that channel of carriers. This is set up by the "doping" of the channel, which is one of the first steps in the fab process.

Transistors that are off by default are called "enhancement-mode". GaN transistors also come in enhancement-mode flavor, so I'm a little surprised by the article. You can buy them, even as a hobbyist, from EPC. [0]

[0] http://epc-co.com/epc/Products/eGaNFETs/EPC2023.aspx

[1] http://www.digikey.com/product-search/en?WT.z_cid=sp_917_011...

I think they actually mean "depletion mode" vs "enhancement mode". It's not so much when the circuit is broken as when the gate is allowed to float.

(The article doesn't even say whether they're talking about FETs or BJTs, but I presume FETs with a super-low RdsOn)

Not exactly sure what the article was going for. Maybe the importance of N-type transistors (they are useful just for being more efficient). Silicon transistors are widely known for failing in a shorted state.