I've seen it done both ways. Picking up the closest five scores to me:
Dover edition of the Marriage of Figaro uses single stems for two (of two) bassoons playing in thirds in bar 292 of the Finale of the second act
Barenreiter edition of the same bar writes it in two voices
Eulenberg edition of Berlioz's Symphonie Fantastique uses single stems in bar 83 for that (for two of four in this case, though)
Eulenberg edition of Mozart's 23rd piano concerto uses single stems in bar 387 of the third movement in bassoon only, for ; clarinets and horns (even though they're also playing in that context - i.e., independent voices with the same rhythm) have it written in two voices
Novello edition of Elgar's cello concerto has the 73rd bar of the second movement written in single stems for parallel thirds and oblique motion into a fifth
I think the cleanest and clearest way is to write it with a single stem if the two instruments move consistently in parallel motion (especially 8ves), and writing separate stems if they are much more separated in terms of direction of motion or the interval by which they move in similar motion. I don't really know, though; I only answered because no-one else did; maybe I'm missing something contextual in each of the scores that contributes to the way it's written and someone who actually knows stuff will post with a definite answer and make me look like a jackass.