This question is impossible to answer without knowing which TPE you mean - TPE is a mixture of thermoplastic elastomers, which is a huge class of compounds.
PVC is polyvinylchloride, which is a specific compound. I found an MSDS here:
My advice is to contact the supplier for each fabric you are considering and to ask them for the MSDS. In that you will see what the acute and long-term exposure effects are for people. "Environmental effects" is a very broad subject, and you are not very likely to find research for any proprietary blends, particulary if they don't come from the US or EU. However, sometimes MSDS list non-proprietary compounds, and you can then check the EPA website for those names to see if there are any reports on broad environmental effects.
If you are also interested in the environmental impact of the entire production chain (which you should be, since end-use is usually the least significant part of that), then you should also ask the suppliers about their manufacturing process, whether they have any "green" certifications, etc. You can look up the patents for each production process (most of the time they will be patented) to see what their raw materials are, and then check the MSDS and EPA reports for those. It is also a good idea to see if you can tour their production facilities, once you know what the potentially dangerous precursors are and how they should be handled. It is easy to temporarily hide bad working conditions, but it is harder to fake treatment and containment facilities. Of course, if there isn't good regulatory oversight, there is a very good chance that the producer will take shortcuts to reduce costs, so keep in mind that what they tell you isn't necessarily going to be the truth.