I recommend that you don’t use a control as your log at all. Instead write a log collection class that has the properties you desire (not including the display properties).
Then write the little bit of code that is needed to dump that collection to a variety of user interface elements. Personally, I would put SendToEditControl and SendToListBox methods into my logging object. I would probably add filtering capabilities to these methods.
You can update the UI log only as often as it makes sense, giving you the best possible performance, and more importantly, letting you reduce the UI overhead when the log is changing rapidly.
The important thing is not to tie your logging to a piece of UI, that’s a mistake. Someday you may want to run headless.
In the long run, a good UI for a logger is probably a custom control. But in the short run, you just want to disconnect your logging from any specific piece of UI.