OmegaT (http://www.omegat.org/) is a popular open-source translation memory.
However, OmegaT is written in Java.
There is nothing wrong with Java in general. However, some 80% of translation professionals in the world have never used anything but MS-Word for their work, and Java doesn't support MS-Word.
TinyTM in contrast supports MS-Word as its first client. We (the TinyTM team) don't particularly like MS-Word. However, we believe that others should take on the "fight" against Microsoft. We want to concentrate on delivering an industry-strength translation memory that will support the 900.000 or so (numbers from Common Sense Advisory) translation professional in the world.
The other main difference between OmegaT and TinyTM is that OmegaT is a single-user desktop application while TinyTM is based on a client-server architecture, allowing groups of translators to work on the same text.
Fortunately, it is possible to combine the best features of OmegaT and TinyTM. The figure above shows how an OmegaT-client might work with a TinyTM TM-server in the future. This way, we could combine the best from the two systems and create a 100% open-source system that is capable to deal with Open-Office (Ooo) and XML files.