Does showing up beat writing in?
Verdict
The clearest, most rigorous evidence on this question is about Congress, not city hall. Congressional staff consistently rate in-person visits and personalized messages as more influential than form emails or mass campaigns. Whether that ranking holds for a city council member has simply never been measured. Grade: MODERATE for Congress, THIN for anything local-specific. The honest answer is that "show up in person" is a reasonable inference for local government, not a tested finding.
What the research says
The Congressional Management Foundation ran nine surveys of congressional staff between 2004 and 2015, asking a consistent question: how much influence would this contact method have on an undecided member?1 In-person constituent visits topped every wave, rated influential by 94% of staff in 2015, down slightly from 99% in 2004. Individualized email was rated influential by around 88% of staff. Form email was rated influential by only 51%, and CMF reports that simply personalizing a form email's subject line and opening lines lifts its effectiveness by roughly 36 to 37%.1
Separately, a genuine field experiment by David Butler and David Nickerson randomly gave half of New Mexico's state legislators their own district's actual polling data before a 2008 special-session spending vote, after surveying 10,690 residents.2 Legislators who received the data voted more in line with their district's actual opinion, while the control group's votes bore almost no relationship to what their constituents actually thought. This is one of the only causal, not just correlational, studies in this research area.2
What it doesn't say
Nobody has run the Congressional Management Foundation's survey on city council members, county commissioners, or mayors. No study measures whether a resident showing up to a city council meeting is more or less persuasive than an emailed comment at the local level specifically. The Butler and Nickerson experiment shows legislators respond to real opinion data, but it doesn't test which individual contact method, call, email, or visit, produces or substitutes for that data most effectively. The often-repeated claim that a legislative office treats one phone call as representing many unheard constituents could not be traced to a primary source and should be treated as folk statistic, not fact.
What this means for you
Showing up in person, and personalizing anything you write instead of copying a form letter, rests on solid ground for Congress. It's a reasonable inference for local government too, since local officials have less staff and fewer filters between them and a resident, which if anything should make individual contact even more noticeable. But that's inference, not local-specific evidence, and you should treat it that way.