Why I prefer EQ cuts for balancing
EQ changes introduce phase changes around the center frequency, which themselves create tonal changes by way of comb filtering.1 Boosting makes the tonal changes that result from phase change more noticeable, whereas cutting can do the opposite.2 Cutting also concentrates the phase shifts on regions that aren’t as crucial. These phase shifts can smear transients too.3 (See Shaping transients to create depth.) Cutting also concentrates pre- or post-ringing on those less crucial areas.4
Use cuts in combination with fader adjustments to address frequency imbalances and Frequency masking. Boosts (by their very nature of making things louder) can be deceptive and more easily obfuscate whether your settings are right.5 Auto-gain can help this is some cases, but be wary of relying upon it.
All that being said, Less is more when it comes to EQ, so doing several cuts to achieve the same effect as one boost may not be the best idea.
Mixing on headphones may be most useful for making cuts at resonant frequencies, this way you aren’t mistakenly hearing room resonances.