First of all, a quote: Duke Ellington said "If it sounds good, it’s good music, and if it doesn’t, then it is the other kind." So if it "sounds better to you," pay attention to that feeling and try to figure out why. But to answer your question:
Are there cases where rhythms between instruments might be completely discrepant?
Absolutely. Brahms often layered instruments playing rhythms that didn't divide with each other—one group playing 3 notes within a beat and another playing 4, for example, at the same time. At the most extreme, there are works where different instruments or voices aren't even supposed to be at the same tempo (in Henry Cowell's Quartet Euphemetric instruments play in different time signatures; in Steve Reich's Come Out a recording of a person speaking is looped, and then a duplicate is played but gets slightly slower until it forms echos and new patterns (
). In another of his pieces, Clapping Music
, two people clap the exact same rhythm, but start at a different point in the pattern, so they combine to form a new rhythm pattern ( ).
For a less extreme example, consider Coldplay's song "Viva La Vida" (
). It opens with a string section playing a rhythm that features some syncopated notes—in the pattern ♩♩♩♪♩♩♪♩♩ the first three ♩s are on the beat, but after the single ♪ the next two ♩s fall "between" beats.
For the first few seconds of the song, that's the only rhythm present. Soon, though, the lead vocal enters with its own rhythm, and at the same time the bass drum starts repeating, one hit per beat, exactly on the beat. Meanwhile, the strings' pattern continues throughout the song. The syncopated notes of that repeating pattern are in direct conflict with the drum's on-the-beat pattern; their offbeat notes emphasize the space "between" the beats, while the drum emphasizes the beginning of each beat.
But here's the thing: that tension is what makes the syncopation interesting. Without a beat for the offbeat to "push against," it doesn't even "feel" syncopated. So yes, it can often serve an important purpose for instruments to have conflicting rhythms.