m6 to M6 progression

It doesn't always happen that way, and the reason for what you've noticed is pretty simple: there aren't many choices.

If you're staying in one key, you have three major chords and three minor ones. So you have nine possible major to minor changes in a major key - three have no common tones (I-ii, iii-IV, V-vi); one has one common tone (ii-V); the rest have two common tones (I-iii, I-vi, ii-IV, IV-vi, iii-V).

Since you can have a change like C-Dm with no common chord tones, there's no implied rule that the root must move to the third. When you have a ii-V change, the root of ii becomes the fifth of V - going the other way, the root of V isn't in ii at all.

That leaves us with the six changes sharing two common tones - which include your examples. But there really aren't six... there are only two. Put C in the place of each major chord and you get:

I-iii = C-Em
I-vi = C-Am
ii-IV = Am-C (key of G)
IV-vi = C-Em (key of G)
iii-V = Am-C (key of F)

Because chords are built in thirds, the only way two chords with different roots can share two out of three notes is if the root and third of chord A become the third and fifth of chord B.

So what you've found is that 2/3 of the mathmatcially possible major-minor changes have two notes in common, and all of those will put the root of the first chord in the third of the second.

But in reality, many major-minor chord changes in tunes will be ii-V changes. Far more than you'd expect if it was all left up to chance... because it's not left up to chance. The more tones in common between two chords, the 'smoother' the change will be to the ear. And a lot of smooth changes becomes boring fast - most two-chord changes will share one note, whether the chords are major or minor. That gives continuity without overdoing it :)

great info there, thanks! :D

Some of what I stated could be wrong, as I'm really just beginning to pay close attention to theory; so please correct anything misstated.

As you've described the root movement intervals (m6 + M6), I believe the progression you meant to write is C#m - A - F#m (not Fm)
(F#m = F# A C#, Fm =F Ab C)

Thanks fretsource, I believe you're right.

Also, I took a moment to work out NoteBoat had said, and have a question:
That leaves us with the six changes sharing two common tones - which include your examples. But there really aren't six... there are only two. Put C in the place of each major chord and you get:

I'm not sure I understand what you mean here. Why is the C(I) used to replace the M chords, making only 2? The rest of what you said makes sense to me.

Finally, the reason I used the progression to begin working on my theory was exactly what was stated: "The more tones in common between two chords, the 'smoother' the change will be to the ear. And a lot of smooth changes becomes boring fast "

With this knowledge of the note movement within the chord progression, what are some ways I can spice up the progression without totally mucking with it? That's the chord progression my bandmate wrote, but I'm the guitarist. How can I make it more interesting while not getting in the way of a melody written over such a progression? I enjoy understanding theory just for the sake of it (weird right?) but it'd be great if I could really use it to apply some new musical ideas.

Edit: I just realized I've only mentioned part of the chord progression. It's a i-bVI-iv-iii-bVII (chords being F#m-D-Bm-A-E; did I write that progression correctly using roman numerals?) That's just to give an overall idea of what I'm working with; again my broader concern is the changes that have 2 common notes.

I'll try to be a bit clearer in what I meant...

A major key has major chords on I, IV, and V, and minor chords on ii, iii, and vi. That gives us nine major/minor combinations:

I-ii
I-iii
I-vi
IV-ii
IV-iii
IV-vi
V-ii
V-iii
V-vi

The same chords will be used in minor/major combinations - but the second chord will come first.

One chord can appear in more than one key - C can be the I in C, the IV in G, or the V in G. Since we're just looking at what happens inside chords, I substituted C for ANY of the major chords (so a IV-ii would be in G, a V-iii in F, etc.).

That shows many of these changes are identical to others... all of the nine possibilites can be viewed as 'key variations' of just five changes:

A major chord going to a minor chord a whole step higher (I-ii, V-vi)
A major chord going to a minor chord two whole steps higher (I-iii, IV-vi)
A major chord going to a minor chord three half steps lower (I-vi, IV-ii, V-iii)
A major chord going to a minor chord a half step lower (IV-iii)
A major chord going to a minor chord five half steps lower (V-ii)

In other words, a I-iii change in the key of C is C-Em; a IV-vi change in the key of G is C-Em. Scale position doesn't matter - there aren't many major/minor changes.

To dress up the progression, you could add some extensions - try adding a sixth or ninth. That gives you two new tones for the second chord, and more variation.

Your numbers are almost right - if you're labeling the chords in relation to the major scale, A would be bvi. Some people label minor keys in relation to the natural minor scale in the key, in which case you'd have i-VI-iv-III-VII. Either method works as long as people know which one you're using... which means you can't mix the two methods.