I'm talking here about negative film.
What you gain is increased contrast.
That increased contrast means that the areas of your scene that would have been rendered as muddy, near shadows if you didn't increase the development ("push") for the film, are instead moved up the film's curve, with more contrast.
The areas of your scene that are below the "detailed shadow" threshold of exposure don't miraculously evidence negative density - they just stay dark shadows.
The problem with any "push" development is that it also affects the highlights of the scene. In some cases, they become so dense and grainy on the negative that you cannot do anything to make them print well.
The loss in highlight quality that comes with a one stop push is most likely the reason that Kodak doesn't recommend any change in development when T-Max 400 is metered at EI 800.
The problem with your test is that most likely you under-exposed your negatives by more than two stops - your meter was fooled by the highlights that were in your scene into setting an exposure that was more than two stops insufficient. That is a common problem in environments that force us to underexpose film and then try to save as much as we can by increasing development.
One solution to the metering problem is to get closer and take a reading from the near shadow areas that you need to make sure are on the negative.