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Is Bitcoin a means of storage of wealth, or is it a payment system?
If Bitcoin has to be a currency, it certainly must be both.The US dollar is a currency and is neither.
It's certainly not a storage of wealth (which is a weird concept, you can't store an abstraction like "wealth" any more than you can store "love" or "respect"), but it is a payment system. It was a payment system long before credit cards and electronic payment processors, long before commercial use of electricity
The irony of your post is the exact reason why the block size debate is going on. No one can answer what Bitcoin is. Yes is acts like a payment system, but if one were to hold their coins then it acts as a storage of wealth.