Shaheen is a larger player than Trey Burton is. 6'6" 270 lbs More similar to Travis Kelce or Zach Ertz as far as his build. Burton is listed as 6'3" 236 lbs.
Zach Ertz missed two games last season game 9 against Denver and game 13 against the Rams. He was injured in week 12 against Seattle and only played part of that game.
Trey Burton
game logs as you can see Burtons best games were game 9 against Denver 4 targets 2 receptions 41 yards and a TD. Game 12 against Seattle 7 targets 4 receptions 42 yards. Game 13 against the Rams 6 targets 5 receptions 71 yards 2 TD. Coincidence? Of course not.
Those 3 games were 55% of his targets 48% of his receptions 62% of his yardage and 60% of his TD for the whole season.
You see a similar pattern in 2016 with Burton having good numbers in game 2 and 3 of that season when Ertz was out of the line up.
Talking about how much the Bears paid Burton is a total red herring in my opinion. It is not representative of what he has produced in his career so far. I think Burton is really overvalued in fantasy circles since the signing and Shaheen is being overlooked.