It's important to remember that the voicing of the chord is only one variable.
Everything from the amp settings, microphone choice, microphone placement, control settings on the guitar, string gauge, pickup type, pickup height, the room in which you record, and the guitarist her/himself will also play a role—in many cases, a bigger role—in the overall sound than the voicing of the chord, especially if you're using overdrive.
The two most typical ways to play Am—at least when I play guitar—are:
x•===• nut •--••• 5th fret
Though it seems these chords appear to have very different voicings, take a look at the constituent notes. The open chord is A2 E3 A3 C4 A4 while the barre chord is A2 E3 A3 C4 E4 A4. The only difference is the addition of E4, which is there as a strong harmonic of E3 anyway. If you analyze all the voicings, you’re going to find mostly the same set of notes.
You can argue, of course, that A2 played on the sixth string sounds different than A2 played on the fifth string. Sure it does, especially clean and in isolation. In comments, you mention that the guitars will have overdrive. Distortion and overdrive add noise and natural compression, minimizing the difference in timbre. Placed in the context of the whole mix, you’re not going to hear much, if any, difference. It’s better to choose a voicing based on playability so the guitarist stays in rhythm and tune more easily.
That being said, extreme differences in chord voicing will, of course, make a difference. An open Am sounds different from Am played by barring the top three strings at the 17th fret, as a guitarist might do in funk or reggae music. EQ cannot make the one chord sound like the other.
EQ is better used to cut frequencies on one instrument which interfere with the same ones on another. EQ can only cut and boost frequencies that are already present. It can not and does not shift them from one octave to another.
If you want the guitars to sound distinct from one another, focus on choosing different tones. Maybe play one clean and one with overdrive or one acoustic and one electric. Or play different parts of the chord on different guitars; perhaps an A5 power chord with distortion on one guitar and the top 3 strings barred at the 5th fret on a cleaner setting with stereo chorus.
In short, I think you’re overthinking the choice of chord voicing. Focus on the mix and how the overall instrumentation and arrangement serves the song. If it sounds good, it is good.