I nearly always use Magnum for bittering especially for lagers as it does not add any noticeable flavor to the brew leaving the later hop additions to shine. The same cannot be said for most high alpha hops which almost always contribute flavor although a different flavor contribution to the start of the boil than say a dry hop addition of the same hop, Citra being a prime example of a high alpha hop used mainly for dry hopping. So yes, changing the bittering hop in most cases will change the flavor of the resulting beer, sometimes for the better, sometimes for the worse.