I have access to the paper. The device is interesting, but as usual journalists want to inflate the balloon some more...
They report a maximum of 16.2nW, open-circuit voltage of 899mV, short-circuit of 107.4nA. To give hackers a reference, in its current state, you'd need something like 50,000 of them to power a single 0.85mW Arduino chip.
In the U of Missouri article they say "The radioisotope battery can provide power density that is six orders of magnitude higher than chemical batteries", but as far as I can see from the article they're not talking about their own battery; it's a general statement quoted from an old paper (F.K.Manasse,J.J.Pinajian,and A.N.Tse, IEEETrans.Nucl.Sci. 23,8601976).
The article in question is "Radioisotope microbattery based on liquid semiconductor" (Applied Physics Letters 95).
I found this company, http://www.betabatt.com/index.html BetaBatt that makes nuclear powered batteries. They don't give the amps or volts either but, it does say,
"[beta batteries can be] Paired with chemical batteries for high current, limited duty cycle applications BetaBatteriesTM increase shelf life and ensure readiness by acting as a trickle charger, thus enhancing capability, reliability and useful life."
In other words this dime sized battery probably doesn't have enough current to power electronics continuously w/o some help.
No, that says nothing about the current and voltage. It could trickle out a teensy bit of current for a very long time, which wouldn't be useful for e.g. a laptop.
I believe "a million times as much charge" refers to the total energy content in Joules. The parent was referring to voltage. The original press release from missouri.edu:
I don't think it does... ...charge is more like the total energy stored in the battery. Amps and Volts will tell you how fast that power can be used. A battery can have a million times the charge but if it can only release that charge over 100 billion years then it isn't going to be able to power small electronics, like cell phones for example.