Sunnyvale and Mountain View aren't really different rental markets, though, so I'd be surprised if the difference in rent increases you saw between the two are related to differences in new housing permits.
Put another way, restricting housing supply in Mountain View likely impacts rents its socioeconomically similar neighbor, Sunnyvale.
They are, though. I wouldn't have expected it, but I was just looking at Craigslist now and rents in Mountain View seem to go for about $700/month over roughly equivalent housing in Sunnyvale. I'm in a pretty old 2BR right next to the Mountain View border for $2600; the equivalent would be a 2BR in the California/Escuela area, which rents for about $3300/month. Perhaps it's just my neighborhood (rents in new construction near the downtown areas are about $4500 for a 2BR in both places), but there's a similar differential among 1BRs north of Central: $2500-$2800 in MTV, $2000 in Sunnyvale.
Among likely differentiators: 1.) Traffic. If you're traveling to Google or Facebook Sunnyvale adds an extra 15-20 minutes to your commute. 2.) Schools. They're better in Mountain View, at least for now, though both regions are rapidly gentrifying. 3.) Cachet. Mountain View has the name because of Google. Sunnyvale doesn't really, and also feels like more of a sterile suburb than a lively community. 4.) Shuttle stops. I don't know exactly where they are now, but that'd explain why the downtown areas go for relatively equal expensive rents, while my neighborhood (which AFAICT has no tech shuttle stops anywhere near it) rents for a lot less than other neighborhoods in the area.
Those factors do make sense, although I'd think Sunnyvale would have a shorter commute to employers like Apple.
I definitely don't have a nuanced enough understanding of the difference in civic liveliness of the two cities - and resulting desirability - they both always felt pretty suburban to me. But I've never lived in either one.
They definitely are - two years ago I left a previous place that had jacked up my rent for a 1 bed/1 bath place to a little over $2600, and was frustrated by the housing market in Mountain View. Most places were charging over $3k, with some going even over $5k. I ended up settling in Sunnyvale for a 2 bed/2 bath place for $2700.
Put another way, restricting housing supply in Mountain View likely impacts rents its socioeconomically similar neighbor, Sunnyvale.