When you play them right on top of each other, the three notes which are a half step lower do seem to sound sadder in comparison, but I think that says more about descending vs ascending tones rather than the key itself.
Also, it's easy to play "random" chords from a tonality and end up in a different mode without even realizing it. E.g.: A minor (the key, also known as A aeolian) has the exact same diatonic chords as C major (but the reference, i.e. tonal center, is A instead of C).
A large part of tonality is chord position in the piece, which is also greatly influenced by dynamics, melody, accompanying instruments, harmony, harmonic progression (both immediate/local and global)...
Also: Cmaj7 (the chord) is C-E-G-B and Emin6 is E-G-B-C (notice the similarity?), but E-G-B-C can also be interpreted as Cmaj7 in first inversion depending on context. Sometimes roots are omitted from chords so E-G-B (Emin at first sight) could be interpreted as Cmaj7(no root). Just like C-E-G could be a rootless Am7 (A-C-E-G with omitted A). They are often used as substitutes of one another in jazz.
Music is just too complex and musical language (chord names etc.) is just a hack developed around traditions and conventions, not science. It's mostly notation of intention, since everything can be twisted to mean something else.
The more music theory I know, the less definite answers to musical questions are.
C major has the exact same notes of A minor, and C minor/aeolian has the same notes of Eb major/ionian (and 5 other modes with different qualities: F dorian, G phrygian, Ab lydian, Bb mixolydian, D locrian... all have the exact same notes).
Even if you think of C aeolian when playing you might be implying a different tonal center, depending on your emphasis, and therefore a non-aeolian progression.
Your ears can latch to any tonal center depending on exact phrasing. With no harmony there is no clear tonal center (and even with harmony, it's easy to switch between related modes, even unkowingly, because they have the same notes _and_ the same diatonic chords).
> But if I just play ascending thirds (R 3 2 4 3 5 4 6 5 7 6 R) in C-minor
Are you playing that in a 3/4 rhythm? (R b3 2) (4 b3 5) (4 b6 5) (b7 b6 R) the downbeats are R-4-4-b7 (no characteristic minor tones) your ears are hearing the minor tones as passing tones. Since aeolian has no leading tone (natural 7, one semitone away from R) the tonal center is even more ambiguous.
You might be hearing that as Bb mixolydian: (2 4 3) (5 4 6) (5 b7 6) (R b7 2), downbeats on 2-5-5-R which is _the_ canonical major jazz progression (ii-V-I). The phrasing implies ii-V (ambiguous if major V or minor v)-v (minor due to b7 of I being b3 of v, establishes mixolydian)-I. V-I is a pretty strong (if not the strongest) tonality indicator.
Bb mixolydian is a major mode, hence why it doesn't sound particularly minor to you.
Try playing the C minor with ascending thirds over a C harmonic minor _progression_ while emphasizing the V-i cadence and the characteristic minor tones (namely, b3 and b6). Notice I said harmonic minor progression, which has a leading tone to strongly stablish tonal center (which is what it was invented for).