There are some very core differences here. The key though is what Bitcoin and Ethereum stand for.

Bitcoin wants to be a currency, plain and simple. Its protocols are as Plain Jane as they should be for allowing for the transaction of funds back and forth. And for that reason it is also pretty battle tested.

However, it is certainly NOT a stable currency in the least. No true currency can have volatility like Bitcoin. Comparatively Bitcoin is a "safer" bet than the other alt coins, but that's like saying eating 50 Habenero peppers is safer and milder than eating 50 Ghost Peppers. Sure the latter is twice as hot, but does that really say anything about Habanero's potency to bust a hole straight through your gut? :)

Ethereum is a platform, not a cryptocurrency like Bitcoin. As a platform it opens developers up to so many options to build on top of it in areas that can, but are not limited to currencies exclusively. And that means that there is more breadth for Ethereum to spread its wings, which is why the valuation of it has been increasing so rapidly. With major MNCs joining the Enterprise Ethereum Alliance and so many ICOs building off of it, it won't be surprising for the Flippening to occur sooner rather than later.

With that said, because Ethereum can do so much, it is also prone to bigger bugs and possibly harder scaling issues with the blockchain being taxed like we have seen recently. Plus, there is concern whether it truly is decentralized since Vitalik really has a strong say in terms of the direction the platform takes. This is partly why Ethereum Classic exists, to truly allow it to be decentralized.

There is so much more that could be said here, but that's the gist at a high level.