Sounds stupidly basic, but we often forget that when you do any kind of parallel processing you are
summing two signals. You are going to get both destructive and constructive interference, meaning some frequencies are attenuated while others are boosted. Sometimes, the results are unexpectedly good, sometimes they're unexpectedly bad, and sometimes just plain unexpected. It's what makes experimentation fun!
This phenomenon bites me more often than I like to admit. Why is the snare suddenly too loud? Oh, yeh, I just ran a send from it to the reverb bus. Duh. Everything you run to the reverb bus gets louder.
However, running
identical signals to two busses should only make it louder. If it also affects tone, then there's something else going on. It
could be a plugin that's not being properly latency-compensated, but more likely one of the two signal paths has some kind of filtering happening.