Vertex colors will be preserved if you use a format which supports them (e.g. .FBX, .WRL, .BLEND, and point cloud formats). The OBJ format can also be encoded to include vertex colors in some applications.
If vertex colors seem over-saturated or "washed out", try switching your color space between sRGB and linear in 3D Settings → Scene. By default, we choose sRGB. You can also improve color quality using Post-Processing Effects.
Vertex Alpha is supported and can be enabled or disabled with the Use alpha toggle.
Vertex colors are compatible with textures, and the colors will be mixed. If parts of your model are unexpectedly dark, you might need to disable vertex colors in 3D Settings.