When you are playing auxiliary keys, you are just that - AUXILIARY. You are not supposed to make your 'voice' heard, but are supposed to compliment what is going on. Auxiliary, by definition, means that the song can go on perfectly well without you - you are there to add flavor and fullness.
I play both roles in my church depending on the service and my style and what I do has to be changed to fit the situation (Our lead pianist is a classically trained, plays mostly just what is written on the page and can square off the funkiest of songs and I am a bluesy by-ear player). If you are like I am an can't stand a clean 1-3-5 chord playing behind someone who knows nothing else, learn the chords they use and change the voicing of the chords when you are playing pads or Rhodes behind them. Adding a 2nd here and a 9th there can add complexity to the song and fill out the sound.
You have to be willing to submit to what is going on with the other instruments in order to play an effective aux role. LISTEN. LISTEN. LISTEN. There are times where it is too crowded already on a song without added noise, no matter how skillful. Find your places to come in and out of the song - even the best guitar solo in the world would get tired to your ears if it went on continuously throughout an entire song.
If the lead keyboardists style is classical, funk, gospel, country, whatever - then that should also be your prevailing style for that song. Remember, you are there to compliment. I don't agree that you are there to backup the lead keyboard player - the aux keys is a different instrument altogether even though it looks the same. You are there to compliment EVERY instrument in the band. You get to be a cello complimenting a bass player, be a steel drum player riffing off the drummer, be an oboe player putting a theme or melody above the choir, be the violin that sings part of the melody with the lead vocalist - what fun. Don't be a competing piano player - what's the point in that?