What do you think? Which is more important, being able to produce clear, well-defined fronts of your notes, or having a voluptuous sound? Actually, both are part of the same thing. If it's a quality note, it starts that way.
Like percussion instruments the trumpets must be able to function as rhythm kings. Good drumming is about definition, and so too the brass needs to be clear, energetic and on the beat, not blurry and behind. As attractive as a pleasing tone is, most conductors can be satisfied with clarity and precision from the brass.
We've played the 10-second game before for audition preparation. That is, playing only the first phrase or so of each excerpt in order to gain instant control. Now we need to play the split-second game. That is, play only the very start of the first note, nothing more. A warm up note is not allowed. The first note must be a winner.
Here are a few pictures that might help sharpen up your entrances: the beating of a snare drum, the banging of the glockenspiel with a steel-balled mallet, a pin prick, the uncorking of a wine bottle, the tip of a sharp long thin sword, the tongue of a rattlesnake, the anchor point of a compass, the tip of a syringe, etc. You get the idea. It's about nails, sharp ones. A cotton ball penetrates nothing. Choose a dart. Don't think about the Pillsbury Dough Boy. Think Dracula! Unleash your killer instinct as you perfect the clarity of every note.
So, go ahead and have your nice sound, but put an edge on it and be able to slice it up into tiny pieces able to project well into the audience. Before sauntering onto the stage, catch a glimpse of yourself in the mirror. Frown a bit, stick out your tongue as far as it goes, and bring it to a point. That tiny tip is about to do battle. It's the one instrument that didn't cost you anything, so train it, sharpen it, and use it!