Currently the Jenkins tests and some of the Pywikibot travis jobs use nose, which includes some logging, but doesnt include timestamps. Timestamps are especially useful for the server side team when tracking down problems (e.g. T114824).
However many of the Travis-CI jobs only use unittest/unittest2, and one of the main advantages is that nose doesnt show the test method name if the test method includes a docstring. This makes it more difficult to find the test method, which is useful if attempting to re-run a specific test method, especially if it fails.
https://gerrit.wikimedia.org/r/#/c/244951/ proposed to use nose for almost all Travis jobs, however it was voted down (-1'd) because of this limitation.
There are several nose plugins that provide test method names:
nose2 may also be a way forward, except for T115296: nose2 fails to load Pywikibot tests