As someone who's done a lot of Discord RPing because I outgrew the scope of the forum I used to RP on, I honestly think forum RPing is still the superior format. Discord is a black hole for information, you don't have access to formatting, there's less text space, and overall it's way less of a pleasant experience.
Most discord RP servers are setting servers - there will be a specific setting contained inside of the server itself. So for example, one discord RP server may be the setting of an entire magical school, while another may be the setting of an entire multiverse. They don't really contain multiple different RPs, but rather different spaces in the setting itself to do multiple RPs in. This, notability, is marginally harder to do on forums, since you'd need a dedicated subforum for it. (See the persistent forum on here for reference)
What discord RPs lack in quality of life, they make up for ease of access. Not that replicating this is on a forum difficult per say, but it requires a lot more technical knowhow than just using the channel system Discord already has. Sure, you have to get together your own mod team, but most people just get the friends they already know to be on the team itself.
In addition, a lot of people just stumble upon the Discord RPing community (like I did), because they're using Discord already. Meanwhile, forums aren't used as often as they should - insert stumbling upon a forum and seeing a notice on top that "This forum is archived but you can join our Discord" here. This is part of the general internet trend of migrating to social media rather than the creation of different sites. Also, I have talked to Discord roleplayers, some of who have been RPing for years, who do not know that forum roleplaying a thing.
I honestly think that's the main dividing line - Discord RPs are (comparatively) easy to start and easy to get into. The experience is less good overall, but if discord RPs didn't exist, some people just wouldn't be roleplayers.
The biggest problem is that the community and the RP itself come together with a package. If the roleplay dies (like many roleplays naturally do), then the community dies with it. Once the RP server you're on stops having RP activity, you have to go to a different server to seek out more, and that means going to a different community. So you have people going through RP servers just to roleplay, who befriend the people there, only for said RP to die and then to lose most of their friends along with it as the remains scatter. And then you have your general issue of server hoppers - users who are so toxic that they end up getting kicked from most servers they join eventually, so they head elsewhere to cause problems, while the perfectly chill RPers don't change servers unless that RP dies.
Also, the Discord RP community skews younger, aka to teenagers. Even in the supposedly 18+ communities (because people lie on the internet all the time). The environment is, in general, mildly toxic at best, and makes the elephant foot look safe at worse. Should you choose to make your roleplay a relatively public one open to the general RP community, you will end up with a mix of immature teenagers and adults with the attitude of immature teenagers - and that's assuming the server wasn't made by said teenagers in the first place. Not to bash on anyone who is a teenager of course, but hanging out in primarily teen spaces is next to insanity once you go to college/university for at least a year. I also wouldn't have so many complaints over it, if I could find a primarily adult RP community that wasn't mature content focused - but such as discord is, finding that sort of community is hard.
Overall, the format sucks and the RPing community on Discord at large is an irradiated wasteland. The two discord RPs I've consistently stuck into (one of which is still active [and is the current target of my RP obsession tendencies]) are both detached from the Discord RP community, in that they don't use disboard or any other servers to advertise themselves. As a result they were successfully cushioned from the community at large, which is not very poggers.
Most discord RP servers are setting servers - there will be a specific setting contained inside of the server itself. So for example, one discord RP server may be the setting of an entire magical school, while another may be the setting of an entire multiverse. They don't really contain multiple different RPs, but rather different spaces in the setting itself to do multiple RPs in. This, notability, is marginally harder to do on forums, since you'd need a dedicated subforum for it. (See the persistent forum on here for reference)
What discord RPs lack in quality of life, they make up for ease of access. Not that replicating this is on a forum difficult per say, but it requires a lot more technical knowhow than just using the channel system Discord already has. Sure, you have to get together your own mod team, but most people just get the friends they already know to be on the team itself.
In addition, a lot of people just stumble upon the Discord RPing community (like I did), because they're using Discord already. Meanwhile, forums aren't used as often as they should - insert stumbling upon a forum and seeing a notice on top that "This forum is archived but you can join our Discord" here. This is part of the general internet trend of migrating to social media rather than the creation of different sites. Also, I have talked to Discord roleplayers, some of who have been RPing for years, who do not know that forum roleplaying a thing.
I honestly think that's the main dividing line - Discord RPs are (comparatively) easy to start and easy to get into. The experience is less good overall, but if discord RPs didn't exist, some people just wouldn't be roleplayers.
The biggest problem is that the community and the RP itself come together with a package. If the roleplay dies (like many roleplays naturally do), then the community dies with it. Once the RP server you're on stops having RP activity, you have to go to a different server to seek out more, and that means going to a different community. So you have people going through RP servers just to roleplay, who befriend the people there, only for said RP to die and then to lose most of their friends along with it as the remains scatter. And then you have your general issue of server hoppers - users who are so toxic that they end up getting kicked from most servers they join eventually, so they head elsewhere to cause problems, while the perfectly chill RPers don't change servers unless that RP dies.
Also, the Discord RP community skews younger, aka to teenagers. Even in the supposedly 18+ communities (because people lie on the internet all the time). The environment is, in general, mildly toxic at best, and makes the elephant foot look safe at worse. Should you choose to make your roleplay a relatively public one open to the general RP community, you will end up with a mix of immature teenagers and adults with the attitude of immature teenagers - and that's assuming the server wasn't made by said teenagers in the first place. Not to bash on anyone who is a teenager of course, but hanging out in primarily teen spaces is next to insanity once you go to college/university for at least a year. I also wouldn't have so many complaints over it, if I could find a primarily adult RP community that wasn't mature content focused - but such as discord is, finding that sort of community is hard.
Overall, the format sucks and the RPing community on Discord at large is an irradiated wasteland. The two discord RPs I've consistently stuck into (one of which is still active [and is the current target of my RP obsession tendencies]) are both detached from the Discord RP community, in that they don't use disboard or any other servers to advertise themselves. As a result they were successfully cushioned from the community at large, which is not very poggers.