For starters; let's take a look at Ben Chiarot. he currently has 5 goals and 4 assists in 44 games played this season with the Montreal Canadiens. His offensive and defensive metrics are near the bottom of the league and he's arguably not playing up to his $3.5M cap hit. Add that to the asking price (a first round pick and a third round pick) and you have a player that not only has been underwhelming, but I don't think he adds what Toronto is looking for - aside from being a nasty SOB of course.
As a rental on an expiring deal, he doesn't fit the mold of the Leafs' current defense corps. Enter Justin Braun. According to Pierre Lebrun, Toronto could look at acquiring the 35-year old defenseman at or ahead of the deadline.
There are a couple things to consider here: Braun is on an expiring contract with a cap hit of just $1.8M and he could be easier to acquire, likely to go for a mid-round draft pick. In 48 games with the Philadelphia Flyers this season, Braun has 4 goals and 8 assists for 12 points. He also appears to be to have a better defensive game than Chiarot and could provide insulation on the bottom pairing for the Leafs.
If the Buds are looking for help on the back end, the logical, more cost efficient player for the Leafs to trade for would appear to be Justin Braun. That said, only time will tell who the Leafs value more.