WM Recorder and Jaksta should record video as is, so video with the variable frame rate should stay with VFR and video with the constant frame rate should stay with CFR.

WM Recorder seems to be very good at syncing audio and video tracks, but I'm not sure it has something to do with CFR.

Have you tested both programs on the same source? What is the link to the web-page with the video where you have discrepancies?