Tallysticks were a purely virtual money with no relation to any commodity supply with a legal and certification framework backing them up in case of dispute which helps promotes trust which in turn enhances their success. There were also very hard to forge which helped a lot (due to the uniqueness of wood grain when split in 2, the sides could be matched up again later).
In fact tally sticks are pretty much the same as the modern commercial credit circuit mechanism used by small businesses in countries such as Uruguay where the currency had become limited in supply under economic collapse situations. In simple terms someone certifies invoices that the transaction and work was real and these then turn into effective money and can be exchanged as such. This requires support of some trusted agent to do the certification so it relates to real work (otherwise you could just print invoices and screw the system up). Government support massively helps in that they can enforce that large businesses also accept these as valid payment. However, without government support an NGO could also do this but the circulation would be smaller.
http://www.worldacademy.org/forum/commercial-credit-circuit-c3
Bitcoins seem more based on a finite commodity system to me, although it does have one improvement over metal based ones as it solves the supply manipulation problem better as no humans are involved (merchants can't rig the supply for their own manipulations as happened with gold and silver etc at various times in history). However, physical has one advantage in that mining real stuff does represent some actual human work at its initial point (that unfortunately later gets distorted though by 'market forces'). I am not sure how well CPU mining work really relates to this part of the equation of relating to some tangible human activity.
History has swung back and forth between these two popular forms because there are pros and cons to both methods but neither have solved the entire problem of fair exchange and representing production. People lose trust in one and the grass then seems greener on the other side of the fence, but later same problems occur as it hits its natural limitation and so history repeats. This is why you are seeing a massive rise in 'gold bugs' etc as the trust wanes in the national virtual currencies. To me it looks like Venezuela is about to revert to metal backed currency soon as they have nationalised their precious metal industries (i.e. the only way of stopping private merchants cartels rigging the supply) and now recalling all their gold from US and UK etc.
I can think of a few ways to destroy and/or control either type of economy if you are so inclined (often even both due to short sighted selfish nature of greed!). I am not letting on yet the exact mechanisms as I will cover those later in a series I am writing. One of the weakness of purely virtual money such a tally sticks (or current digital money) also happens to apply to commodity based currencies, even if those avoid the other weaknesses. Bitcoin seems to avoid one more common weakness to me but not all.