A kick drum can be loose, tight, deep, percussive, hollow, tubby, thick, light, etc. Do you want it to hit you in the stomach? The chest? The face?
Likewise, a bass could be rough, smooth, deep, throaty, thick, etc. Bass often also has the potential for emphasising the higher-register sound of upper overtones. A bass could be as deep as the stomach (or even lower!), or high enough to be a low-register melodic counterpoint to the melody.
Of course, these are just examples. Kicks and basses can be anything you imagine.
My point is that you need to make a decision about what you’re trying to do with the kick and the bass. They should not only complement each other, but also be appropriate for the production values of the song.
For example, if you want both the kick and the bass to be equally thick and low, the effect will be muddy and confusing if they’re playing at the same time… just as if a guitar solo and lead vocal were to sound similar to each other and be playing at the same time. No matter how you EQ or compress, you will be fighting every step of the way.
The choices you make will determine the kind of processing you need to do.
Personally, I usually take one of two approaches. I might want a deep strong bass, in which case I’ll make the kick weaker and more percussive. Other times I might want a higher, more melodic bass, which allows me to make the kick lower and longer. If I want a strong kick, I need to make the bass higher and/or weaker.
Which approach I choose for a song depends on what I’m trying to do with the song as a whole. For example, if the song has a strong rhythmic element or has a lot of other melodic instruments (such as guitars or keyboards) I’ll usually emphasise the kick and push the bass back a bit. Alternatively, if the song is more sparse I might need the bass to provide much of the harmonic support, so the bass becomes high(er) and stronger, and the kick is lower and more subdued. If I want a heavier sound, I might want the bass to be quite low and deep, and emphasise the percussive nature of the kick (shorter and sharper).