Is using bitcoin for savings a risky choice? I'd like to start saving money and there are a few options. 


Cash provides anonymity but it's very susceptible to steal and I must have a physical space for it. 
A bank account is much safer but I don't really like the system to keep track of my savings. 
An offline bitcoin wallet would provide both safety and anonymity.


It seems the last option is the best choice because the money saved can even go up in value as bitcoin deflates. But, what if it never takes off as a mass used currency? What if it somehow gets deprecated by a similar cryptocurrency?

How big is the risk of saving in a bitcoin address?
Buying bitcoins shouldn't be thought of as savings, it's a very high-risk speculative investment. It could go way up in value, or way down.

Luckily, if you want Bitcoin's power of secure storage without exposure to the exchange rate, you can do that too, in theory at least. Use most of your funds to buy X bitcoins, and use the rest as collateral to short-sell X bitcoins. You'd have to pay a bit more for the exchange, pay an interest rate, and trust some of your money with the platform, and there aren't currently very good margin trading platforms, but it can be done and might be worth it if you're sufficiently averse to the traditional alternatives.