It depends on how do we compare them and what do we want to use them for. Ethereum is better than Bitcoin and Bitcoin is better than Ethereum at the same time.
Theyve made several completely different design choices and as with every choice it opens some oportunities and closes dosens of others.
I would highlight a couple of main differences:
Bitcoin is a currency
Ethereum is a platform for running decentralized apps (smart contracts)
Supply
Bitcoin is deflational
The overall amount of BTC ever produced is limited
And
Ethereum is inflational
The ETH supply in unlimited
Security
Bitcoin is simple and limited
The built-in language is stask-based and stateless
Thats why you can not express a loop and its not Turing-complete (this means, that there are some programs, that are impossible to write)
Ethereum has a rich programming language built-in
The built-in language is Turing-complete (this means that we can code anything we want)
More complexity implies more opportunities to make an error
Bitcoin has a first move advantage
My mom knows what Bitcoin is
The community is a lot bigger
Its easier to get started
There are already a lot of places where you can pay with BTC
Ethereum is less known and younger
It uses move fast and break things motto
It learned from Bitcoin and fixed a couple of issues in its design
The community is smaller and therefore has more developers than speculators
To sum up all:
Theyre not competitors
They coexist and solve different types of problems.
A Turing complete language means anything can be done with it given enough time and enough computing power.
This means that Ethereum has a broader base to build on and a broader market to enter - as it isn't locked to being a value transfer ledger - which is where the analogy of ethereum as a tcp/icp in comparison to bitcoin as your email comes in. Although Bitcoin could be built upon to allow the functionality that Ethereum has - it would be clunky!
The major difference is the simplicity on building on top of ethereum. For example some very smart guys at Slock.it have built a device that unlocks for a period of time on the condition of payment to a particular wallet. So can you imagine paying for an air b and b to turn up at the door swipe your phone and enter - no key handovers but a bit of a bummer if your phone has no juice.
The other set of differences comes in the way Ethereum and bitcoin are built. Ethereum uses ethash instead of sha-256 - which means that individuals can compete in mining it (Ethash is memory hard meaning it needs memory to run - which in turn means it works more efficiently on a GPU ) whilst Bitcoin has ASIC chips that have led to a moore's law race and concentrated mining power!
Ethereum also has a shorter block time than Bitcoin - due to some clever hacking using the ghost protocol - which basically means that forks in the chain are rewarded but don't cause to much of an issue! So Ethereum a transaction should be confirmed in under 20 seconds and with bitcoin 10 minutes... less waiting around.
But at last, I would like to say that investing on ETH will be more profitable.