I am a Kaplan teacher, and have been for 7 years. I can't really comment on Testmasters however, I can assure you that Kaplan uses only actual LSAT questions. In fact, when you sign up for a Kaplan LSAT course product, you will have access to every single LSAT in multiple formats. In your online syllabus, you will have all the tests together with all explanations. In addition to this, we break down some tests into 35 minute sections to practice timing. Other tests we break down right to question type in Logical Reasoning (assumption, inference, parallel reasoning, etc), game type (sequencing, matching, etc) and passage type so that you can practice mastery of different question formats by targetting them. Since I work for Kaplan, clearly I'm biased but when choosing a prep course, you want to think about what you want. If you like to work on your own, you can take an on-demand course with us. If you benefit from a classroom environment, you can take an on-site class. We also have live online classes. Since Kaplan is the biggest (and oldest) test prep company, we are able to devote tremendous resources towards deconstructing the test, and creating a course based on sound pedagogical principles.
Good luck with your LSAT journey!