I haven't used ConvertX for many years, and then only the original free version and the trial that left a watermark. But we have a few members here who use both programs, so perhaps they will chip in.
AVStoDVD is the best free conversion program for making dvd-video that I know of. It has some excellent features, such as allowing dvd-compliant streams to be authored without re-encoding, and it is flexible on output. You can make mpeg files, and elementary streams as well as complete dvd-video. I wrote a guide for it, which you can find here: http://club.myce.com/f32/avstodvd-guide-331620/
The author will respond to any problems you have with the program if you post in his trouble shooting thread over at Videohelp.com. You can find the link to that thread in my guide above.
AVStoDVD does have some weak points, particularly in its ability to handle certain audio formats. DTS HD MA audio (the most common high def audio these days in blu ray) can be a problem. And AAC in mkv files can gum up the works on occasion. The DTS issue was bad enough that I quit using AVStoDVD for conversion of blu ray to dvd-video, and only do that conversion now in BD Rebuilder.
But 90% of the time AVStoDVD will have no problems converting videos. ConvertX will work more often on these problem conversions, but I would expect this as a commercial product.
As a general rule, AVStoDVD can produce slightly higher quality output using the HC mpeg2 encoder (2 pass) than what you see from ConvertX. ConvertX will be faster most of the time.