Summary
Depends on what you're doing. MediaLab can take RTs, but..
Details
Both programs are stand alone, but they do work very well together as complements. Whether you use one or both depends on what your needs are.
MediaLab has more flexiblity and greater ease of use with respect to traditional questionnaires (many closed and open-ended question formats) and multi-media stimuli (movies, sound, html, word documents, powerpoint shows, etc.). You can point and click an attractive questionnaire or experiment together really quick and the data files are very easy to work with as they're horizontal (one row per subject) and ready to analyze in Excel or SPSS.
Its weakness is that all the multi-media flexibility requires that it be a traditional windows program so the precision of timing (both display and RTs) is not great. It's also not great when you have a more cognitive/perception type of study where you have hundreds of repeated trials (e.g., priming/lexical decision style tasks).
This is what DirectRT is excellent for. You define your trials in a spreadsheet (e.g., Excel) so you can use your favourite spreadsheet app for editing the input files (a very nice benefit).
You get total control over timing because it's a DirectX application and not a "Windows" program. Basically, it was created to do what MediaLab can't do well--high precision cognitive/perception, "blocks of trials" types of tasks. Due to the nature of DirectRT experiments, the data files are vertical (e.g., one row per trial).
This means it takes a bit more skill to collapse and analyze the data. Although some tasks could be easily done with either program, one or the other is usually a clear choice. A lot of people use both and embed DirectRT sessions within a more general MediaLab experiment.
That's the gist of the difference anyways..