Did an early ride this morning, uploaded to Strava and had a good look at the website.
As a free user, the ride summary looks the same with the usual segment list, times & achievements. Speed/Power/Temp are still there in the analysis page. Heard a rumour that all heart rate functionality is premium only, but didn't wear a strap so can't comment. Haven't got a cadence sensor currently, so can't even comment on that.
You do still feature on leaderboards, but you can only see "All time" and "All-time (Women)", and then only the first 10 riders.
Your PR time is always visible, but if you're outside the top 10 you can't see your place. The Elevate Chrome Plugin does still seem to show your place but this might be old/stale data.
None of the other segment leaderboards are accessible free, which is slightly disappointing for "People you follow" and annoying for "My results" (although there is a glimpse of My Results if you use the Android app, but not the website).
I have a few mates on Strava and it was amusing to virtually challenge each other on hills and sprints. I'll miss that function, although you can still click into their ride results to see their segment times, and this does still show their PR - so some element of competition is still available free of charge.
Strava has provided nearly a decade of free entertainment so maybe I'll bung them some money at some point.