Similarities:

Both are valuable cryptocurrencies.

Both uses Proof-of-Work mining.

Bitcoin:

The first decentralized digital currency.

Cryptocurrency - A cryptocurrency and worldwide payment system.

Accounts - Just maintains the state of all transactions that are flowing.

Smart Contracts - Though it is based off a scripting language, it has very limited functionality and only a few dozen operations.

Transactions - 3 per second.

Consensus - Time to propagate around the network. Top mining pools control 75% of all mining activity, causes centralization in the system.

Mining - Proof-of-Work is SHA256, ASIC-receptive to mine BTC, 2.5 BTC/block.

Ethereum:

World computer for developing DApps. Currency aspect is just one application of Ethereum.

Cryptocurrency - A cryptocurrency to run the state of machine of Ethereum AND a cryptocurrency traded on exchanges.

Accounts - Maintains proper accounts. Externally owned and contract accounts.

Smart Contracts - Turing complete language integrated within. Programs written in this language are Smart Contracts. SCs are pre-written logic stored and replicated on a blockchain. If blockchains give us distributed trustworthy storage, then smart contracts give us distributed trustworthy calculations.

Transactions - 15 per second.

Consensus - Adopted GHOST (Greedy Heaviest-Observed Sub-Tree) which brings efficiency gains to the Proof-of-Work. Solves the first problem of network security loss by issues stale blocks.