Google's John Mueller said in a video hangout 22 minutes and 21 seconds in that there is no magical SEO advantage when switching from HTTP to HTTPS.
But didn't Google tell us that HTTPS is a ranking signal? Yes, but only a "very lightweight signal" but that may increase over time. It hasn't yet.
Jennifer Slegg first covered it and transcribed it:
I wouldn’t expect any visible change when you move from http to https, just from that change, just from SEO reasons. That kind of ranking effect is very small and very subtle. It’s not something where you will see a rise in rankings just from going to httpsI think that in the long run, it is definitely a good idea, and we might make that factor stronger at some point, maybe years in the future, but at the moment you won’t see any magical SEO advantage from doing that.
That said, anytime you make significant changes in your site, change the site’s URLs, you are definitely going to see some fluctuations in the short term. So you’ll likely see some drop or some changes as we recrawl and reindex everything. In the long run, it will settle down to about the same place, it won’t settle down to some place that’s like a point higher or something like that.
Here is the video:
My thought, if you know what you are doing, do the switch. It can only benefit you if you do it right and in the long run, Google will tweak the signal and give more weight to it.
Forum discussion at WebmasterWorld.