For what it's worth, the e-mail customer service seems to echo the telephone customer service.
My attempts to resolve issues with UA (as a Premier Executive) were incredibly painful. The initial delay in responding to an e-mail has always been 2-3 weeks or more, and respondents to follow-up correspondence have shown no interest in actually following the trail of the previous dialogue. Anything close to resolution has taken months...
In contrast, as a Platinum with AA, I've received non-automated acknowledgment of some sort within a few days, and if follow up is needed, resolution is usually achieved within a week or two. I am not saying that I have liked what AA has had to say, but the responses have always been professional and targeted toward my specific concerns.