Speaking as a brass doubler (trombone is my primary; I play all other brass instruments with varying proficiencies), the main difference between the embouchures for trumpet and trombone has to do with the tone concept.
The trombone itself (and current pedagogy and instrument manufacturing) allows for a very open and dark tone concept, and the fact that tuning can be adjusted easily with the slide helps to allow for this.
If I play trumpet like I play trombone, it will have a very wide open sound, but certain partials will be woefully out of tune. When I play trumpet, I need to treat the oral cavity differently to enable the correction of certain partials with the embouchure. On good instruments less correction will be required, but you still need to be generating the correct amount of tension with your embouchure.
If there are any cons, it really depends on what your level of technique is, what you're aiming for, and how much professional instruction you're getting. Any doubler just needs to remember what instrument they're playing at the time and have a different mindset for each one. If you try to play the trumpet like the trombone, you're going to run into trouble, just as if you started learning trumpet and then played trombone like you were playing trumpet. Private instruction will let you know if you're developing any bad habits on any one instrument.
On the other hand, if you're self taught and just want to play ska music with your friends, chances are your technique isn't on a level where it'll make a difference.
The pros here are pretty obvious: you learn another instrument, you start opening your ears up to that instrument, you get a different perspective on music you already know, and it's just good general music practice to read notes in a different clef and transfer generic musical knowledge from one instrument to another.