AccuFACE 2 does not require facial calibration in the same way as AccuFACE 1. However, you can use Grab Neutral in Motion LIVE to set neutral position, which may help improve the tracking results. See here:
https://manual.reallusion.com/Motion_LIVE_Plugin/Content/Motion_LIVE/2.0/Grabbing-Neutral-Pose.htm
If you notice that the character’s mocap results from AccuFACE2 differ from the original video, you can try switching to a different Facial Profile to see if it improves the results.
1. Test with the same Expression Motion
Instead of recording the expressions directly with AccuFACE, please try applying the same Expression Motion to both characters after recording. Then check whether there is still a difference between the two characters.
If both characters perform the same way with the same Expression Motion, we can rule out AccuFACE as the cause and focus on the characters’ facial profiles or other settings.
2. Try using a different Facial Profile
A character created with Headshot 3 will use the HD Neutral Facial Profile by default. However, if you compare it with our default Aaron character, please note that Aaron uses a facial profile specifically customized for that character.
The comparison below should help illustrate how the same character can produce different facial results when different Facial Profiles are applied.
(NOTE: This character is made by Headshot 3)

Since every character has a different facial shape and eyebrow position, the same Facial Profile may not work equally well for every character. In some cases, a custom Facial Profile may be needed to achieve more natural and accurate facial expressions. That’s why I mentioned in the previouis answer that try applying another facial profile and see if it works for your specific character.

These should help determining whether the difference is related to AccuFACE itself or to the Facial Profile being used by the specific characters.
Since the CC5 HD avatar (the left character from your attached screenshot) includes more facial morphs on his face, He can perform more facial details. Please check again your right avatar.
If she is not HD character, you can also turn it into HD avatar, see here:
Upgrading CC3+ to CC5 HD Characters | Character Creator 5 Tutorial
https://courses.reallusion.com/home/character-creator/motion-pose-and-facial-expression?v=upgrading-cc3-to-cc5-hd-characters-|-character-creator-5-tutorial
And here below are some related manual pages for your references.
CC5 Extended Plus Facial Profile Introduction
https://manual.reallusion.com/Character-Creator-5/Content/ENU/5.0/05-HD-Character/Extended-Plus-Facial-Profile.htm
Character’s Expression Upgrade (HD Animation)
https://manual.reallusion.com/Character-Creator-5/Content/ENU/5.0/05-HD-Character/Expression-Upgrade.htm
HD Wrinkles
https://manual.reallusion.com/Character-Creator-5/Content/ENU/5.0/04-HD-Contents/HD-Wrinkles.htm

