EVM – Why Does a Solidity Throw Consume All Gas?

With an exception, as with throw, all effects (including events) of a transaction are reverted, except for the payment to the miner. So there would be no benefit in firing an event before a throw.

Possible Alternative

If full reversion via an exception isn't required, an error code might be usable.

Example:

contract C {
  function foo() returns(int) {
    if(msg.sender != owner) {
      Error("User not authorized")
      return -1111;  // some error code
    }
    // sender is authorized so do stuff
  }
}

Events can't be accessed by contracts so the error message is more for the frontend. If the message is just for the frontend, consider using a pattern of eth_call before an eth_sendTransaction (call vs sendTx explained here).

The eth_call before eth_sendTransaction pattern would look like this frontend Javascript code:

// `contract` is an instance, from web3.eth.contract(...).at(...)

if (contract.foo.call({from: eth.accounts[0]...) === -1111) {
  // example only of how error could be dealt with
  alert("User not authorized");  
  return;
}

// user should now be authorized (though it is possible another transaction may have changed `owner` in contract `C` after above eth_call and before this upcoming eth_sendTransaction)
contract.foo.sendTransaction({from: eth.accounts[0]......)

That said, there can be cases where creating an Error event is desired. For example, if your DApp wants analytics on how many errors have been encountered, how many are unauthorized errors, etc an Error event could be the way to go.

EDIT: When https://github.com/ethereum/solidity/issues/1686 is implemented, the example in the question would look like:

require(msg.sender == owner, "User not authorized");

Solidity didn't offer an exception management mechanism as try/catch (for Java/c#).

due to an invalid EVM code, throw consumes all provided gas terminates and reverts all changes to the state made by current contract execution and to Ether balances. this concept intends to prevent spamming the network.

in the Yellow paper it is mentioned that :

Just as with contract creation, if the execution halts in an exceptional fashion (i.e. due to an exhausted gas supply, stack underflow, invalid jump destination or invalid instruction), then no gas is refunded to the caller and the state is reverted to the point immediately prior to balance transfer (i.e. σ)

as an information for the “intrinsic gas too low” message

Mist checks the amount gas without executing any code and it tells you that the transaction will fail because you didn't provide enough gas to execute the transaction.