Discord is more for short, instant messaging type information that is better for communicating with people in real time.
Forums are a much more natural and versatile way of separating and discussing various topics.
With forums, any time Jays news hits, let's say a medium sized trade, a new thread will pop up and if you log on two hours after the news hits, it will all be neat and tidy and you can participate in the entire discussion. The discussion will last for a couple of days (or as long as necessary) and when it reaches its natural conclusion it will fade away.
If a trade happens on discord, there's a flurry of messages right away. Some of the comments might be good, but if you aren't on when that comment is posted, it's going to get buried pretty quickly. On top of it, all of it will get jumbled into the same channels as other news that hits. Just not an easy way to discuss baseball.
The only way it would be better would be for GDTs really. Those are probably the worst aspect of this forum, it's filled with knee jerk reactions from casuals. Discord wouldn't really improve that aspect of it, but it would allow for better real time communication which would make a big difference for a quickly moving game.