"Is Bitcoin more like a currency or more like a company?"
Here is my most simple reasoning to "proof" that Bitcoin is better described as a company than a currency.
First: It is stupid to call it a currency, simply because Bitcoin fulfills pretty much all criteria of money but the two related things that distinguishes currency from money (the fact that a currency is issued by a state and the fact that there can only be one currency within a currency zone; sometimes the definition of currency is equal to the def. of money but that doesnt help us here) is not the case with bitcoin.
Second: It is a matter of fact that there can be many crypto ledgers all providing the same service (this wouldn't make sense if we said "it is a matter of fact that there can be many crypto currencies all providing the same service since currency implies that there can only be one; but currency is only an analogy not reality). These different cryto ledgers compete with each other. What makes Bitcoin be the most used is the network effect but this is not what makes a currency being the only money used. The force of the state (to pay taxes with it) makes currencies being the only money used in a currency zone. These observations alone indicate / prove that Bitcoin might be more accurately analysed as a company (value transfer is the service the virtual and decentralized company is providing) than a currency.
Here is my most simple explanation in how far Bitcoin is a DAC:
"Decentralized Autonomous Company" (DAC) is only a metaphor, an analytical framework. This metaphor applies to Ethereum, Bitcoin and most Bitshares projects alike. The difference is the complexity of the service that is realized and the way it is implemented. The DAC analogy/metaphor was first introduced by Stan Larimer back in September 2013.
Bitcoin can be described as a DAC:
a) It is decentralized insofar as a government could shut down a lot of miners but the network would continue to process transactions because one could never shut down all miners.
This can be argued to a degree because the growing centralization of ASIC mining.
b) Bitcoin is autonomous because it does not depend on it's creator to keep on running.
This can be argued because the Bitcoin foundation has de-facto control over decisions to change the code.
c) Bitcoin is insofar a company as it provides a service (The Bitcoins network allows for "value transfer" with applications in remittance, e-commerce etc.), it has expenses (electricity costs of miners) and "employees" (miners), it has revenues (fees) and Bitcoins can be seen as shares in the "Bitcoin value-transfer-network" which go up in value if the network is used much because the amount of Bitcoins which are necessary to make a transaction over the network is limited. This again can be argued on several levels.
Of course, no analogy can ever be a perfect description of the (code and social) reality. An analogy can be helpful explaining things but holds the potential for misunderstandings if the analogy is taken too far. The analogy doesn't shape the reality.
I have tried to define DAC here more accurately: https://bitsharestalk.org/index.php?topic=7730.msg102386#msg102386
Hope it helps with creating material.