Love MUS here too. The biggest difference is that TT is a spiral program. Where MUS is a mastery based program.
You can go to TT website and let your child try some samples. (I looked at it, because we have several friends that use it and love it.) But it was not for us. Way too much review. My son got frustrated with it. MUS teaches a concept then you practice mastering that concept then there are a couple of review areas during the week. TT has a lot of review.
In fact in the demo we did out of over 68 problems only 4 were on the subject of the lecture all the others were on reviewing concepts.
You can also go to MUS site and watch a Demo video that shows you how it works. We have used it for 5 years, and it has given us a great foundation. (Some people say it is behind -but usually that is because they are spiral programs that introduce concepts early, but do not actually have kids master them.) Where as MR. Demme doesn’t do that. When he introduces the concept, he has children master the understanding before proceeding. Then he buildes upon that -sort of like building a house from the foundation up.