I was hesitant to move our site to Discord, so honestly, we use both? We don't permit IC chatting, to prevent people from falling into the trap of quickfire RP scenarios that ultimately drive attention and desire away from posting. Our discord server is also private. I didn't really like the idea of having guests pop in, even to an isolated channel. Maybe I'm just weird that way, but it felt invasive to me! So, the cbox is on the site and free for anyone to post in. Once a potential member's first character has been accepted, they receive an invite to the site discord!
Discord is super easy and mobile-friendly, and the ability to categorize different channels is pretty amazing. We even have one channel with a bot installed (Talos) that allows members to run word wars to sprint out posts. 🙂 We used to use Skype for large group calls, but it's honestly nice not to have my phone buzz in the middle of the night like "HFTA IS CALLING! WAKE UP!" haha. Now, we can just pop into the voice channel when we feel like talking/hanging out, or stick to text if we need the quiet.
It's really all up to you and how your board functions. Everyone has different needs.