The proposal for distinguishing based on "closing the tab" is a bit tough, as the JS dialog code doesn't know if its tab was closed when it's told to cancel the dialog.

The metric that I've used in the past in making arguments in Intents is DIALOG_BUTTON_CLICKED (that the user clicked a button and dismissed the dialog in that manner) vs everything else (which is either that the user went away from the page or killed it in some manner, or perhaps the page closed the dialog itself by popping another one). I would highly recommend using DIALOG_BUTTON_CLICKED vs everything else.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/52531c3d814ec1e66f086cbb4d4f781ebf61bea8

commit 52531c3d814ec1e66f086cbb4d4f781ebf61bea8
Author: Yao Xiao <yaoxia@chromium.org>
Date: Mon Aug 27 19:50:51 2018

Log JS dialog dismissal cause to UKM

Bug:  864194 
Change-Id: I84311118bdfc6921875741fa6ba31ba38bcf1fb6
Reviewed-on: https://chromium-review.googlesource.com/1185217
Reviewed-by: Robert Kaplow (slow) <rkaplow@chromium.org>
Reviewed-by: Avi Drissman <avi@chromium.org>
Commit-Queue: Yao Xiao <yaoxia@chromium.org>
Cr-Commit-Position: refs/heads/master@{#586377}
[modify] https://crrev.com/52531c3d814ec1e66f086cbb4d4f781ebf61bea8/chrome/browser/ui/javascript_dialogs/javascript_dialog_browsertest.cc
[modify] https://crrev.com/52531c3d814ec1e66f086cbb4d4f781ebf61bea8/chrome/browser/ui/javascript_dialogs/javascript_dialog_tab_helper.cc
[modify] https://crrev.com/52531c3d814ec1e66f086cbb4d4f781ebf61bea8/tools/metrics/ukm/ukm.xml