Picking out which instrument takes the solo is less a question of pros and cons and more a question of arrangement. Quite simply, I think you already know everything you need to make this decision, you're simply having a hard time picking from several good options!
As with any other time you're picking which instrument gets the lead line, selecting who plays a solo is a matter of instrumentation. If you have a clear idea of the texture you want, then give the melody to the instrument that handles it the best just as with any other melody. The fact that it's improvised is an unimportant detail in terms of deciding on tone color.
I don't think I'm going to say anything revolutionary here, but here are my first thoughts about each of your options, especially in the context of a high-energy piece:
- A trumpet solo can be high-pitched and easily cut through the rest of the band. You can have the lower and middle registers doing all kinds of crazy things in the trombones and saxes without burying the trumpet.
- A trombone solo will need more space. The trombone and sax sections both tend to occupy middle registers, and the high registers of trumpets can draw attention away from the soloist. So it's more difficult to write backing parts to a trombone solo. That said, you can give bright stabs throughout the chorus, injecting punchy energy in a way that trumpet solo is too overpowering to allow for. It's a different kind of aggressive energy!
- Saxes can cover just about any range you want depending on which kind of sax you give the solo to. But saxes are capable of a very different kind of energy than brass. Brass instruments are most typically heard in orchestral and stately settings, so even in a swingin' big band piece, they have an air of formality to them. In contrast, saxes are much more closely associated with dance and commercial music than orchestral traditions, so they can either go Sexy Saxman-wailing or draw out a more emotional and delicate woodwind sound. Both can be powerful and open up different textural options than brass.
Again, you already know all of this. If you can't decide because all your options seem good, that's great! That means you can't mess it up ;)
One option you haven't mentioned is to write out the full chorus with no solo part notated, but include directions to the band that someone should take the solo during that section. Whoever solos will simply improvise instead of playing what's written, and the rest of their section can sit out to give them space or pencil in a part that matches one of the other sections. Think of how bands use a Real Book lead sheet for both straight playing and improv.
In other words, you'd be outsourcing this arrangement decision to the band! This can feel lazy since it's avoiding making the decision yourself, but it also allows the band to consider their own unique sound and the strengths of their players in a way you can't. So while it's not necessary to handle it this way, it's not wrong to, either.
