As Nick pointed out, context is everything. When you are first starting to learn vibrato, you typically have one "flavour" at your disposal. Usually it's something like Rocky Road blended with Cotton Candy, which isn't a combination that works all that well or is appropriate to too many situations. After a while, you develop a palate. Maybe your Vanilla is a subtle moderate speed, moderate width vibrato that warms up a few notes here are there. Maybe your Chocolate sounds like Gary Karr. Maybe your Strawberry is lightening fast and really tight. When you have different flavours, they compliment the music you are playing. Just as there is a wide selection of music, there is a wide selection of vibrato.
Typically the slower the tempo, the slower the vibrato. Dynamics tend to have less influence, where the period or country the piece was composed in, and the desired effect has a lot more. Listen to some film scores that use strings, and you will encounter the big grandiose vibrato in picturesque sweeping shots where the camera is on a helicopter flying over the landscape or the love interests have finally realized they can never be apart and slow motion run to each other from opposite sides of a park. The tight and fast vibrato comes in the quite, creeping up on someone, not sure if there is a demon around the next corner, sit on the edge of your seat and try not to jump scenes. A lot of white light and maybe some aliens? Probably pretty wide and slow to give you that "spacey" sound.
I'm using the example of film scores (with actual orchestras instead of midi strings that have come a long way in recent years but tend to have less of a tonal palate to draw from) because they tend to be very obvious in what emotion/effect they are trying to achieve. If you feel the music you are trying to make is associated with a particular message/feeling, draw from what you are used to hearing when you watch those things on screen.
Keep in mind that Baroque/early music typically didn't use much if any vibrato, and no vibrato has a very interesting sound that we currently tend to under utilize.