If you like how Mailgun has done things over the past two years (under private equity ownership after separating from Rackspace) you'll continue to enjoy using their service.
I view this more like a Series C/D venture investment than I do what most folks consider a "traditional PE investment" though the early stage folks won't look at Mailgun because of the startup -> acquired by public company -> carve-out cap table.
Otherwise Mailgun managed to handle being acquired by Rackspace [1], and then spin back out of Rackspace [2] reasonably well...
[1] - https://www.mailgun.com/blog/mailgun-is-being-acquired-by-ra...
[2] - https://techcrunch.com/2017/02/22/mailgun-there-and-back-aga...
https://techcrunch.com/2019/01/23/idera-acquires-travis-ci/
https://news.ycombinator.com/item?id=19218036
https://www.reddit.com/r/programming/comments/b6l559/travisc...
Modified on: March 13, 2019
The original founders have moved on and put a second company through YC S15 called Gravitational: https://www.ycdb.co/company/gravitational