You already know that you can do breakout sessions in Zoom. Webex is following suit with its latest release! According to the Webex help site:
Breakout sessions are smaller groups that are split off from the main Webex meeting. They allow a subset of meeting participants to collaborate and share ideas over audio and video. Use breakout sessions for workshops, classrooms, or for when you need a moment to talk privately with a few participants, outside of the main meeting.
This is part of the updates coming to Webex in September. There will be even more upgrades as well, including larger audio/video preview panels, more controls within the panel of the call itself, and additional virtual background images.