I could go on and on about the benefits of the new system, but the biggest difference is visibility. When you have one scheduler with a paper calendar, only she can see the events. It works fine if your only goal is to reserve the building and avoid conflicts. But no one else can see the calendar.
With the new system, everyone can see the calendars they want to see. So our high councilors know when to come to Stake PEC; our young men know when to come play basketball; our Relief Society sisters know when the General RS Broadcast is, and if there's a dinner scheduled beforehand. Everyone can see where the event takes place and what date and time, and other details about the event.
Lots of people have smartphones that sync with the calendar (which lets them also set alarms for events); others go to LDS.org to see the calendar; ward bulletin editors can go to LDS.org to see the events and summarize the upcoming events in the weekly ward bulletin.
There are benefits to the distributed scheduling as well, but if I were to pick the biggest benefit, it is that the entire ward and stake can see the events.
Questions that can benefit the larger community should be asked in a public forum, not a private message.