Which is better??

for an eleven year old which is better a trumpet or trombone?

Trumpet

Probably the trumpet just cuz it's hard getting slide at the exact place for a note. But a trombone is concert pitch instrument so there's no need to transpose if you're playing with a piano or in a band.

A lot of people would say trumpet on this one.
But personally I think either is best.

Trumpet is good because it's easier to learn the fingerings, and it's smaller.
But remember that once you get into harder levels of music, trumpets can sometimes have pretty high notes that can be hard to reach. But this is tha same with trombone, only trombone is lower in general.

And people argue that it's hard to learn all the slide positions on trombone, but I disagree with that. It took me a day to remember all the slide positions, and another day to make sure they were in tune. Trombone is also a more rare instrument, not many people play it. Therefore, it's easier to get into honor bands and solo festivals since you don't have much competition. On the other hand, there are a LOT of trumpet players. Most band teachers prefer to have more trombones.

neither is better, if you like the sound of a trombone better, play the the trombone, if like the ound of the trumpet, play the trumpet

It is entirely up to the player. Try both, whichever one feels better, or is more enjoyable, is the right horn. Both of them are easy to play and very difficult to master...