How long have you been working on trumpet and how are you doing with it as far as tone production? If not long and not well, than in my opinion, I think your best bet would be to go for trombone. I don't actually play trombone or baritone horn, so I'm not familiar with that size mouthpiece and embourchure, and I've never used a slide, but I know how a slide works and all the positions. I'll bet if you handed me a trombone I could figure it out and get used to it in under a minute. I play trumpet, horn, and tuba now, so I'm close to having the whole brass family covered. In my experience, tuba turned out to be LOADS easier than trumpet, and I found it easier to get a prettier, more consistent tone on the horn than the trumpet. So in other words, I find the embourchure for the trumpet much more demanding than any of the other brass instruments, and if you want to learn one quickly and sound better than crap in under a month, go for trombone if you haven't already started trumpet, it'll probably take less time to develop a better embourchure for it.
In terms of which instrument is better or more agile or whatever, they are not the same instrument so you really can't compare them. It's not like comparing two different trumpet mouthpieces based on tone, agility, and range. The trombone in general is an octave lower, so much different character, while the trumpet is high and in your face. The trombone also has a slide, which makes tons of things possible that you can't do on a trumpet, the only disadvantage is when you want to try to play in tune you need to be more careful. Valves are best for agility and right-on intonation, while the slide can be used more expressively, creating effects that take years to develop on trumpet. So they both have their place, no one is better than the other. You'll also need to consider what part you'd rather be playing - trumpets have the melody more often than the trombones, so you're more pressured to get things right, whereas the trombones are more of a counterpoint, harmonization, or bass line most of the time, and don't get as much attention.
No matter what you do, play around on both, see which is more comfortable, and give them both a chance.
Since you're setting out to learning a brass instrument, one tip I can provide from my experience with trumpet (2 yrs), horn (1 yr), and tuba (5 months) is
learn to play loudly. And I mean as loud as all HELL. Completely blast for maybe 2 - 3 minutes a day or per practice session. Maybe blast as part of your warm-up, but just a little bit, a couple notes is enough. The reason I say this, is because students picking up a brass instrument, especially if they don't have a teacher and are self-taught, tend to fall into using a different embourchure setting for different ranges and dynamics. Like when I try and play a low C on trumpet at pianissimo ( pp ), I ended up using a completely different embourchure than when I played fortissimo ( ff ). You shouldn't. Through the entire dynamic range of any brass instrument you need to maintain a consistent embourcure or else your tone will not be consistent. So what you do is play some note as loud as you can, so you can just hit it hard, with that brassy edge, and not sound like crap, then play that same note very quietly without taking the mouthpiece away or moving your lips away from that setting. The embourchure it takes to play that loudly is the embourchure you should use all the time, no matter the dynamic. Since if you play a certain embourchure in a soft passage, then you have a sudden very loud accent, what are you going to do? Shift your embourhure from your 'soft embourchure' to your 'loud embourchure'? I don't think so.
Plus, playing super loud every once in a while during your practice session keeps you thinking about the
air that you need to use all the time, which is a lot. You need more air than chops, and beginners tend to forget that. This is something that's been working for me, but not neccessarily for everyone, so any seasoned brass players who might have something to say on this, I encourage them to do so, for I am not a seasoned brass player.
Again, this is all personal experience, you don't have to listen to a single thing I say.
