One way to make your MIDI sequences more realistic is to try to make them "breathe." By shaping your lines into phrases and adding pauses (breaths) you can achieve a more musical performance - especially if you don't record in real-time.
No breath, constant tempo - Hmm, 37 sec. on one breath?
No breath with fermatas - 45 sec. Circular breathing?
Breath/Phrasing added. More musical? Realistic? Should the "breath" be a bit longer?
Breath, fermatas, with reverb. A more realistic sound?
By the way, you've probably noticed that the trumpet sample used in these examples has a "warbly" vibrato. Does this vibrato make the sound more or less realistic to your ears?