I tend to go with John Allen and play faster notes on the E string closer to the end of the fingerboard with only very long sustained notes bowed half way towards the bridge.
The three basic variables, bow speed, arm weight and contact point are painfully evident on the E string, especially for clean note starts. Generally across the 4 strings I find the thicker the string the less bow length that is required to support the same tone and projection. The bow will move faster across the G string and closer to the bridge to support the faster vibrations (stay away from the end of the fingerboard!). Conversely I might be down to playing the same length note using half as much bow on the E string, and closer to the fingerboard, to match the sound quality.
Try playing faster and faster notes on the E string and you have to shrink bow length and move gradually closer to the fingerboard, always listening for quality and clarity of tone and watching the width of string movement. Match your bow length to the increasing flexibility of the string. Stay in the "comfort zone", not too close to the frog and not further out than half way. Around the balance point is the magic place, so easy for string crossing too.
Another trick to produce even tone across all strings is to play flat on the hair on the E string and, without altering the bow hold, roll across to play more on the top side of the hair on the G string (which does not need as much hair contact?)
It takes any bowed string note about the first 10 vibrations to reach its full tone according to Knut Guettler. The open E is vibrating about 41.7 times per second so fast notes will never fully sound. What can be heard first in fast passages is the mechanics of starting notes with the tone of notes following slightly later. The 1/4 second lag in full tone might be a good reason for not using much (or any?) vibrato on E string notes.
Happy hunting!
DP