Quick tip:

Use inversions for a deeper sound and more tone

How

This principle applies for any chord, check that you're using the right inversion and neck position for that chord. They all sound different and what's more, they sound different on different guitar/amp/speaker combinations.

Need a dropped-D/7-string sound very quickly, play an inversion starting on the A on the 6th string. It will sound deeper than the standard of playing the D major as a barre chord on the 5th fret.

From this:

e-5-

B-7-

G-7-

D-7-

A-5-

E---

to this:

e---

B---

G---

D-4-

A-5-

E-5-

It's not as wide as the initial chord due to the lack of higher notes, but it can sound really meaty and works very well with overdrive/distortion and humbuckers. Use single-coils with slight overdrive and you have a good basis for alt-rock.

The D-minor variant is a bit more of a stretch:

e---

B---

G---

D-3-

A-5-

E-5-