Ethereum has faster transactions than the 10 minutes of standard bitcoin protocol. How do the transaction fees compare at the moment if you translate the price into a comparable currency like dollars or euros? Long-term how are they likely to compare?
Every computation on the Ethereum network cost gas, so do value transfers like on the bitcoin blockchain.
Every computational step, or OPCODE requires a specific amount of gas (which is hardcoded). You pay for gas using ether. To determine the fee you pay you calculate:
required gas * gas price = fee
For example a simple value transfer cost 21000 gas, the current gas price is dynamically set by users and miners and is currently ~0.00000005 ether, so the value transaction would cost ~0.00105 ether or $0.001 to $0.002 USD at current prices. Current BTC transaction fees vary anywhere from $0.01 to $0.09 USD
Users can set the gas price they are willing to pay and and miners can set the minimum gas price they are willing to accept. This creates a dynamic market, which allows ethers "fee" to be dynamic and adopt to ether price swings.
In short, in Ethereum the fees are paid in gas and calculated based on contract code execution complexity, in bitcoin the're based solely on transaction size.
The fee for a value transfer is
21000 gas, you need to check the current gas price on the Ethereum Stats and then multiply the gas cost for the gas price or you can use this gas calculator that also does unit conversion.
For Bitcoin you can check the fees explanation page and formula from the bitcoin wiki.
This is the formula is:
priority = sum(input_value_in_base_units * input_age)/size_in_bytes
The recommended bitcoin standard transaction fee is 0.1mBTC (10000 satoshis) even if the minimum fee around ~0.055mBTC. The fees rises if you aggregate multiple inputs, to produce multiple outputs instead, because their size is smaller (1/4) compared to an input, the amount to pay is smaller.