Hmm..
Both had a great year in 1997.
Both switched from babyface to heel.
Both created great heel factions.
Both also missed time due to injuries.
Bret won the WWF title twice in 1997 (Feb. and Aug.)
Shawn won the WWF title twice in 1997 as well (Jan. and Nov.)
Shawn also won the Tag Titles (May) and European Title (Sept.) in 1997.
So now let's look at their best matches from that year. (not counting Montreal)
Bret:   Final Four Match
           Austin-WM13
           Austin -IYH April
           Austin-Street Fight Raw
          10-Man Tag-IYH July
          Taker-Summerslam
Shawn:   Sid-Rumble
               Tag Title w/Austin vs. Owen/Davey
               Austin-KOTR
               Mankind-Raw Aug
               Taker-Ground Zero
               Bulldog-One Night Only
               Taker-HIAC Badd Blood
Pretty even there, both had some of the best matches of their careers in 1997.
So we go to promos, where although Bret improved and was able to cut some good heel promos I still think Shawn's promo game in '97 was just on a whole 'nother level.  Promos were never Bret's strong suit, so I would give it to Shawn, even though I feel '97 was probably Bret's best promo work of his career it just wasn't as good as Shawn's.
This is really close overall but I would say Shawn had the better year...slightly.  Better Matches (IMO) Better promos, was a better heel, and I feel that DX was more impactful than the Hart Foundation was.  Bret was hot for a couple of months after he turned heel but by mid August he was already losing heat as champion and was in a nothing mid card feud with the Patriot while Shawn was red hot as a heel and in the main event feuding with the Undertaker.