What are the implications of running a portrait vs. a landscape format press?

Since no one else jumped in with an answer yet... assuming all things being equal and printing the same final page size, a landscape press will have an easier time maintaining perfectly consistent heavy coverage area and solids than printing the same size solid on a portrait press since the length of ink to be maintained is less (say 12" vs. 17.5")

As mentioned above, a landscape press has to roll a shorter distance so therefore should be easier to roll a solid, The advantage of a portrait press is that you only have to control the ink/water over a shorter distance, usually meaning less ink keys.
Also worth bearing in mind is that if you wish to back up work using the same plates (a 2pp job) on a portrait press the job must be in the middle of the sheet and the paper needs to be all the same size exactly if you want good register front to back

To add to the argument when you back up (work &Turn), the landscape option is by definition more accurate as there is more front lay edge to align the sheet before it is in the grippers and the minimum trailing sheet to control as it passes through the press.