I will offer a little different perspective based on the teaching I received. My trombone teacher in college said that the trombone is the closest thing to the the human voice of any instrument. He had his students listen to hundreds of hours of live and recorded vocal performances. Singers can have commanding tone, but they can also be seductive, grating, persuasive- basically the whole range of human emotion. Remember that the trombone's first use was to play with and in support of vocal music. Listen to this and see how seamlessly the trombones blend with the vocalists.
https://www.youtube.com/watch?v=p29zSdXQhsQ
Whenever I play trombone I try to hear someone like Titta Ruffo or Martti Talvela in my head. To me, trombone playing is first and foremost about picking from a range of tonal colors and the way I shape a phrase follows from that.
Tonally, the euphonium is kind of a one trick pony in comparison. Before you jump all over me I will add that it is a really good trick. I don't think there is another instrument that can project and fill a space like a well supported euphonium. Roger Bobo called the euphonium, as well as the British Eflat tuba, somewhat monochromatic and always pretty. Always pretty was not exactly said as a compliment. Throw twice as much air as needed into a trombone and it will get loud and nasty. Throw twice as much air as necessary into a euphonium and it will be loud, but still pretty.
Now to why I think this one trick is such a good one. If you want to make pretty music the euphonium provides you with a great tool kit. The higher resistance compared to a trombone allows you to make barely audible ppp entrances. The fact that you can dramatically increase volume without fundamentally changing the tone quality gives you tremendous dynamic range for shaping melodies. Add in the facility afforded by valves and there is a lot you can do in service to music.
For me, I look at trombone playing as more a visceral experience and euphonium playing as more cerebral. I am not about to give up either of them and I love them both.