Allen,
You've got several things going on with your system. First off, when you say 'DVD analog, DVD Auto, or DVD DTS', it sounds as if you are describing the input options on your receiver or processor for the DVD input, correct?
If so, in order to hear the DTS soundtrack, you will need to select either Auto or DTS mode. Most receivers these days will have no problem at all just leaving it in full Auto mode all the time. Some older receivers back in the first generation of DTS machines, had a few glitches and it was sometimes necessary to put the machine manually in DTS mode. Frankly, I'm not sure why manufacturers still include a manual DTS mode if the Auto mode works all the time. But, I digress...
You mention you have a DTS decoder built into your DVD player. This complicates things. Since your receiver has built in DTS decoding, it doesn't really make sense to use the DTS decoder in your DVD player. You probably COULD do it if you really wanted to, but there are no advantages.
So, you may need to go into your DVD player's menu and adjust a few things. I've never fiddled with a built in DD/DTS decoder on a DVD player, so I don't know if you have to disable them for the other outputs to work properly. However, two settings you will definitely need to get right are the Dolby Digital and DTS output settings. The option you want is typically called bitstream - other choices may include PCM or off.
The primary difference between Dolby Digital and DTS is that they use different algorithms to compress the audio so that it fits in a much smaller space than would be required for the type of audio present on a standard CD. DTS has traditionally used, and to my knowledge still uses, much less compression than Dolby Digital. Put more simply, DTS uses more storage space to recreate the same soundtrack. Many feel this is why DTS soundtracks can and do sound better. I could go either way. There are excellent examples of both DD and DTS movie soundtracks. The one leg up that DTS has (at the moment) is that it has a true discrete seven channel format - DTS 6.1 discrete. Dolby Digital EX uses a matrix rear center channel, similar to how ProLogic works for the front center.
I've just got my rear center speakers working, and I like both DD EX and DTS-ES. If the recording engineers do their job, I can't tell much of a difference at all between the two.
I pick DTS because I find that in general, the soundtracks are higher quality. I figure this is more likely due to the care spent in producing the sound track rather than the inherent superiority of the DTS format. I also pick DTS because they are the underdog. Dolby has been around since the 70's, DTS only since the early 90's. Always root for the underdog, even if it's only just as good!
Aaron Gilbert
Me? I think DTS sounds a little better than Dolby. 
