The Italian Espresso National Institute
has a long list of criteria (7g coffee, 88C, 25sec, 25ml, yada yada) that specify Italian espresso. While these specifications represent a good starting point for espresso, I doubt that anyone here follows these criteria blindly for all coffees and all machines.
Different baskets (and groupheads) allow for different doses. For some double baskets, a 14g puck tamps so far below the rim that it is clearly a downdose. For others (I'm thinking of small diameter lever baskets), 14g represents the maximum that you can pack into the basket before the puck hits the shower screen. Claiming 14g as the standard dose for all double baskets simply does not work.
Coming back to the original question: in my experience, anything that affects espresso flow will also have an impact on taste. This includes basket geometry. If you have two baskets of different size but similar flow characteristics for a given dose, then the effect will be minimal. But if the same dose leads to different flow in different baskets, I would expect the taste to change as well.