Concerning some microbeam sources (they are not exactly X-ray 'tubes') I heard some times ago about the metal jet microfocus X-ray sources (developped by Bruker, I think). You can goole 'metal jet microfocus X-ray sources' or 'liquid jet x-ray source'.
You can also find some information at XENOX, they (can) produce some focussing/ collimation devices (see e.g. http://www.xenocs.com/applications/microdiffraction.html)
Kevex (Thermo Scientific) and Varian are two standard suppliers of point-projection x-ray tubes. As to "brightest", that is a difficult question to answer because you don't mention the requirements on wavelength, monochromaticity, source size, etc. Usually, short of a liquid metal jet source (which is very limited as to materials and therefore output wavelengths), a rotating anode will put out the most photons, but probably not from a very small source, so it depends again on what you require.
There are also conventional micro-focus sources available (e.g. not liquid jet). Yxlon are one supplier (they took over Feinfocus's microfocus tube business): http://www.yxlon.com/Technology/Microfocus-X-ray-tubes
Phoenix are another - they make tubes in which the final window doubles as the electron target giving a very wide angle beam.
Both these suppliers (and also Excillium) tend to be used in imaging applications. Yxlon and Phoenix make their own micro-CT systems based around their tubes.