So I'm attending a sort of "private music academy" owned by my church right now. It's a cool, and I'm improving my overall performance and arranging skills. But Im wondering, from you musicians:

On your main instrument, do you find it most important to be fluent with all chords or with all scales?

Obviously, both are most desired, but I noticed that for myself, doing scales on piano doesn't help me anywhere near as much as learning my chords, and that on trombone, playing arppegiated chords/triads doesn't do so much as scales do for me.

How about you?

A lot of context is needed to answer a question like this. But without any context, the short and simple answer is both are important. You've observed the idiomatic capabilities of both the trombone and the piano, those will vary from instrument to instrument. Ultimately, it would be helpful to know what your goal is.

davdud101
On your main instrument, do you find it most important to be fluent with all chords or with all scales?

 
....for me it's being fluent on the relationships. Those can be applied to both chords and scales. One could easily argue that my term "relationship" is really just "scales" and I guess they would be right - but it could also be "modes", "progressions", "intervals", etc... It's just in they way it is visualized.
 
My visualization is the number system, however any formal training is likely going to balk at that so forget I said it
 
Education... You will relate to some instructors, your will not relate to others. Don't get frustrated with the latter... Music can be approached in so many ways and when you find an approach you can comprehend - run with it. After 35 years of playing I am still amazed that I can always learn something from anyone. Learning music truly never ends.

Learning chords without being proficient at scales is like learning to write without knowing the alphabet.

The OP sort of hit on the context that came to mind for me initially. The instrument itself can limit ability for chords, but in a broader sense chords drive the framework and scales the detail to me. Many songs can be performed with chords and vocals alone (if the instrument will support it, and depending on genre). Scales (melody) used are constrained in a way by the underlying chords. They really intertwine based on the instrument.

From the perspective of guitar I often stress chords first, since people get inspired by being able to "play a song" early on.

On your main instrument, do you find it most important to be fluent with all chords or with all scales?

 
Yes

As already pointed out chords make a FRACK of a lot more sense if you understand scales. Chords are constructed by combining notes in a scale. Chords are defined by measuring the distances between the notes and comparing them to the Major scale. Chord progressions/movement are created/defined by how they move around/fit into the diatonic modes (or how they DON'T fit into them in some cases).
Practicing scales helps develop the ear and provide the physical dexterity to quickly and accurately play chords and chord progressions.
 
Chords actually are scales... just with some notes omitted and sometimes played all at once (but not always as is the case with arpeggios).
 
However scales are pretty lame and useless without chords propping them up whereas chords can stand on their own in a composition.

I was taught a few scales.. just what I need for the music I play no more.. then I was taught Chord Theory which means I can play any possible chord because I understand what makes them from knowing my scales. 

As a French horn player, I think ear training within a harmonic context is a great way to practice both of these things.

Working out melodies based on a progression is a great exercise. Or picking out a particular scale degree within each chord of a progression (e.g. 3rd of chord #1, followed by 5th of chord #2, 7th of chord #3, or any other random combo) can help you think on your feet and also help you practice intonation within chords (lower them major thirds!).

^^ excellent advice for improvisation.