Having used both systems, I think that Discord's all-in-one comms approach seems to be the way things are going. It's greatest strength is that it only takes one click to switch to any voice or chat channel which is especially handy for assembling a wing or raiding group. It's also easy to invite people to the server, and there's also a limited web version for people who want to chat but can't/don't want to download any software. At least two of the guilds that I've been in have switched over from TS to Discord. Discord's biggest downside is that its interface is
different - not necessarily a bad thing, but it takes getting used to.
TS still works well for voice, but only for voice. It's clunkier to use, and in previous guilds, we wasted a lot of time getting people to switch between servers for joint operations with other guilds. This probably won't be a problem in E:D though.
In short, if you only need voice and only have a small number of people, both work fine. If you are a member of multiple guilds and have lots of friends, I think Discord is the better option.
Like evovi though, I don't use voice comms all that often as it isn't always convenient.