String tension is a very interesting thing. On very old instruments or one's with marginal structural stability and not having rock solid glue joints, placing a set of heavy tension strings on it can and does put a lot of stress on the wood which could possibly lead to the failure of the instrument. If you place a low tension string on an instrument you will immediately notice a quieter sound as opposed to the medium tension or heavy tension string.
Majority of all strings used are medium tension. It seems to be a good comprimise between the higher tension (brighter louder-harsher) string sound which a dark mellow instrument might need to sound its' best and the low tension string set which an instrument that has a beautiful bright high pitched sound quality to it and the player would like to tone down a touch would have.
Synthetic strings will continue to stretch if placed under too great a tension, steel core or metalic core strings will not stretch that way and thus will put incredible loads on the instrument if tuned up to the proper pitch as opposed to lesser tension ones.
The vibrational movement of the string is greater on a low tension string vs the high one and thus would require a touch more clearence on the fingerboard in general. Heavy handed players would benefit from a high tension string since they hammer on the strings harder and deflect them more. Like Doug Kershaw did.
The high tension will produce the sound and the frequency but will be a brighter sound and require a heavier bow touch. A very light weight bow on a synthetic core string or gut string and an instrument that already has a bright and bousterous sound would greatly benefit from a low tension string set. The dark mellow violin with a high tension string set would benefit from a heavier bow with greater pressure from the bow but the speed of bowing would be comprimised.
Quite a balancing act if you ask me. That's why majority of strings sold are medium tension. Getting into wolf tones and such stuff makes the choices even harder. An instrument made say 50 yrs or more ago was designed and built for a gut or synthetic string set since the metalic core strings weren't made yet for it, so they would probably (generally speaking here) sound their best with a low or medium tension synthetic core or gut core string set.
The newer violins which have been made with more modern materials and techniques will handle the harder strings like Helicores and Preludes easily.
Most of this is my opinion achieved from my own research and may not reflect the misguided opinions of others.