I feel like that there is actually a subtle difference but I also think that I might not ever have thought about it had I not seen this question.  In that sense, I appreciate the question.

Are we native speakers required to be aware of the difference?  No, I do not think so unless one wants to write professionally.

I think that "[N1]を[N2]と<b>した</b>[N3]" sounds **more indirect, oblique or roundabout** regarding the [N1] than in "[N1]を[N2]と<b>する</b>[N3]".  The former with した sounds just slightly more "informal" or even colloquial/conversational at times because of the indirectness.  The latter with する has an "official" feel to it. 

> A)「[山田]{やまだ}をリーダーと<b>する</b>サークルを[作]{つく}る。」

> B)「山田をリーダーと<b>した</b>サークルを作る。」

There is a little more emphasis placed on the choice of 「山田」 as the leader in A) than in B), but both are correct and presentable .

> C)「[環境問題]{かんきょうもんだい}をテーマと<b>した</b>テレビ[番組]{ばんぐみ}をみる。」

> D)「環境問題をテーマと<b>する</b>テレビ番組をみる。」

In C), it sounds like the speaker would watch TV programs that are more loosely related to environmental issues than implied by D).  In D), the speaker seems more selective of the programs being about environmental issues.