I think this question is most often addressed according to the particular Jewish traditions of the family. Those who strictly adhere to a specific shidduch process that dictates the choices available to the bride and groom (think members of a classic Chassidic dynasty) will more than likely have a far greater say in the match than families which follow one a less clearly defined.
As to the unasked question of which approach is superior in building a bayis ne’eman, etc., I haven’t even the slightest clue. Personally speaking, though, I feel there’s a certain romantic appeal to the notion of someone blessed with Divine insight matching people to their ideal soulmates.