I can't speak to the timed access, but I use Teachable and LeadPages, and am considering ClickFunnels. You may be comparing apples and oranges here, because LeadPages and ClickFunnels serve two very different purposes.
LeadPages is meant to create landing pages and boxes to capture leads. Example: you can use one of their templates to create a webinar registration page, or offer a free content upgrade (aka lead magnet). People provide their email address in exchange for your content. Most folks hook up LeadPages to an email system (maybe CRM) to then at a minimum send a thank you email, and at most take them into a funnel outside the LeadPages platform.
ClickFunnels is a marketing automation system, sort of more like Hubspot or Marketo, that allows you to create and manage the entire funnel. So instead of having to integrate multiple tools, like LeadPages, email system, newsletter, CRM, etc., ClickFunnels will allow you to do everything on one platform.
Hope this helps!