With Atlas, I filed a form and received an email with docs (to sign) a few days later. I got my Certificate of Incorporation and a bank account (got blocked, but that's a different story) the same day I signed docs. Then, they invite you to issue the stock via the web form, and that concludes the process on their end.
The only hiccup was with receiving an EIN confirmation later, so I had to call IRS so they could fax it to the third-party designee.
Haven't used Clerky, but the biggest perks with Atlas are a bank account (which is generally a pain to open for non-residents) and $5k AWS credits.