That is the trick. To be able to choose notes outside the chord tones or the scale that will make or break your improv. You need to understand chords to play well using scales. You still have to choose the scales that fit over the chord progression or it will sound terrible.
Knowing scales to the point that you can use bits of them to bridge between chord tones is also a good thing to know. It keeps going back to them being part of the same thing called music. Focus on one without losing sight of the other just like you said.
After studying them both at length, I found playing through chords and adding bits of scales where needed much easier for me personally. You will just have to play with them and see how they blend for you and the kind of music you want to play.
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