A point of clarification needs to be made about THX. THX is not, and never has been, a recording format in the sense that DD and DTS are. Tomlinson Holman is the audio engineer who, in cooperation with George Lucas, developed the performance specifications that came to be known as THX (an abbreviation for 'Tomlinson Holman's Xperiment'). Holman was also known for developing the well-regarded Apt/Holman preamp in the 1970's.
At the time Tom Holman developed the THX standards, the quality of sound in many theaters across the country was mediocre to abysmal. Holman and George Lucas wanted to ensure that the sound quality of the original "Star Wars" movie contributed to the overall impact of the film. The THX specs that were subsequently developed were to ensure that theater sound systems met the performance parameters needed for high quality theater audio. (The THX standards specified factors such as the number and type of speakers; the amount of amplifier power needed to drive the speakers, and the way the amplifiers responded under peak load; the kind of theater furnishings; etc.)
There are many audiophiles and home theater experts who believe that THX spec's are largely irrelevant for the home environment. THX has made a bundle of licensing money from manufacturers that want to have the THX logo on their equipment, because uninformed consumers are willing to pay more because they incorrectly think that THX is necessary for the home theater environment. In most cases, it is largely meaningless. (For example, there is a THX version of the Bryston 4B-ST power amp that is identical in every respect to the "standard" 4B-ST, except for having a 12 volt switch that turns the amp on automatically when the preamp is turned on. This auto turn-on feature is a THX spec, which even the totally uninformed consumer ought to realize has NOTHING to do with sound quality.)
Many surround processors have a THX equalization circuit that can be engaged or disengaged. The purpose of the THX post-processing circuit is to slightly roll off the high frequency boost that is often added to movie films to compensate for the loss of the highs in a large theater. These high frequencies can lend a somewhat shrill quality to movies seen in the home, so THX post-processing provides a way to correct for this.
As others have already commented, DD and DTS are likely to be around for quite some time. The general consensus among critical listeners is that DTS provides better audio quality than DD, because it has a higher data rate than DD. DD, however, has the lion's share of the market. DD and DTS have essentially killed off SDDS, Sony's movie sound track processing that required its own proprietary soundtrack playback system in the theater.