The latter statement really calls the first into question. Similarly, they care about my vote, except to the extent that it's completely lost in the noise of thousands of other votes.
However, there's an obvious difference when one sends letters or emails to the federal level. When I've gotten responses, it's always been at least several weeks later, and sometimes several months. The messages I've received have been loosely related to my original message, but they have never addressed any actual point I might have made. I'm not feeling the love.
It's systemic lack of involvement that's causing the most issues in American politics. From the top with "lifetime senators" largely immune from their constituencies, and from the bottom with voter turnouts under twenty percent.
They listen; they just don't have the staffing to write an individual response to every comment. Unfortunately, they listen by having a staffer say "We had X people contact us in favor of this; Y were opposed." But they do listen. Or: Our voices have been abstracted into sort of a reverse-poll thanks, in part, to technology.
As an anecdote, the only time I had a staffer actually respond to my opinion with more than "I'll pass along your comment" was during the SOPA/PIPA call ins. The staffer I spoke to was clearly (and kind of understandably) irritated with the volume of calls and was somewhat short with me. I think everyone views that whole thing as an exception, though.