Actually, it's explicitly stated the Dragons can absorb each other's power the way you do, and that they need to practice their thu'um to strengthen it. Individually, each of them has hundreds or thousands of years of experience with the meaning of each thu'um, and theoretically you could become as powerful by spending a long time building your understanding (and thus strength) in each thu'um like the greybeards do without killing dragons. It's much faster to just take what they know, though.
As for absorbing changing the absorber, well, I'd argue it doesn't. Probably, powerful and high-ranked dragons have devoured plenty of their kin but not changed their nature much, if at all. Then again, as the Dovahkiin is already very draconic in nature (strongly inclined to power and leadership/ruling/mastery), any changes might not have much effect. However, it is explicitly stated that fully understanding the meaning of a thu'um involves changing oneself to reflect its meaning, so every thu'um you learn changes your beliefs and worldview a bit.
Absorbing hundreds of dragons' souls might not change your mind much, but Unrelenting Force makes you resist the world more and Dragonrend makes you fully aware and understanding of your own mortality (as well as making you more hateful).