What is the difference between ojdbc6.jar and ojdbc7.jar?

Note that another difference between ojdbc6 and ojdbc7 is the supported Oracle version.
Specifically ojdbc7 does not support Oracle 11.2 or 11gR2 whereas ojdbc6 does: source.

The included ojdbc6.jar is the latest 12c driver. The only difference between ojdbc6.jar and ojdbc7.jar is that the latter one is compiled with Java 7. Since DB Solo is at least for now using Java 6, it can only include ojdbc6.jar. In terms of functionality the versions are identical. Link

For completeness, note that the number in the filename is NOT the version number of the driver and ojdbc6.jar version 12.x has a weird difference respect ojdbc6.jar version 11.x: newer versions do not truncate or set to "00:00:00" the time component when called with setDate and getDate methods, so you should pay attention to the version number too (you can find it in the manifest as "Implementation-Version"). See this post for more details.