my organization would like to let users (anon and auth) be able to submit a request for a workshop via a drupal webform which would then be approved or denied based on various criteria by management.
Would it be better to have the webform submission trigger civi to record a new event, or activity (i.e. email response) from an admin?
A drupal webform cannot create an event (it can register a person for an existing event tho... is that what you meant?). It can create an activity, which, even if you don't use it as part of your approval workflow, might be useful just to record the fact that the person submitted a proposal.
It's hard to say what you "should" do because you haven't described exactly what your end goal is. Is a workshop ultimately going to be a CiviCRM event, with participants registering, etc? Or something else? I'm not sure that you necessarily need to be creating anything in Civi for your purpose. Maybe all you need is the webform submission. Or activities might work well for you if you create a few extra activity statuses like "Proposed" "Approved" and "Rejected". Or if you wanted to get really detailed in your record keeping, you could have the webform open a case, which would let you record all your back-and-forth (as activities) and the details of exactly when and why the session was approved or rejected.
Seems like the bottom line is that you'll end up creating the actual sessions by hand (as Civi events or whatever else) so that's not really part of the equation here, so you should just do whatever works well for you to record the proposals and manage the acceptances.
Both could work, but it seems closer to the "normal" civi workflow to create an event. If you haven't enabled it already, you should try enabling the satus "awaiting approval", that is linked to an approval workflow that seems to be what you want to use at our org
