[watwut]

Imo, the difference is in the focus. The passive voice version makes the "support of the new constitution" the most important thing the sentence is about. The active voice makes "Thomas Jefferson" the most important thing the sentence is about.

So, it really depends on what the rest of the paragraph is supposed to be about.

[didntcheck]

Which is why the blanket aversion many style guides have to the passive voice makes no sense. Use it when it makes sense to use it, obviously. Often, the subject of the verb really is of little importance, particularly in formal accounts of events