The preferred URL format has changed though your older URLs will continue working for the foreseeable future. The changed format is clearer and
You are correct that you can't use these URLs in IMG SRC tags -- the reason is because they are API URLs and they count against rate limiting and go through the stack to be served. That does not scale. If you're using this method to obtain avatar image URLs you should cache the result. The URLs also invoke a redirect which is not a smart behavior to use for IMG SRC tags.
If you're showing avatars in the context of tweets, the avatar image URL is included in the embedded user object of the tweet. You can also get the current avatar image URL for the user by executing [node:66,title="users/show"] or [node:63,title="bulk users/lookup"]. This API method is most often used for backfilling, updated cached user data, and other indirect uses.