As I understand, Burst is a fork of Next. Which other platforms are forks of Next?
The most well-known NXT fork is probably Waves, although newer versions have "driven away" a lot from the NXT codebase. Another newer NXT fork is Heat, but it has also some own extensions.
NEM was originally also planned as a NXT fork but the development team finally opted for an own implementation/codebase based on "Proof of Importance", a kind of "weighted PoS".
Then there were some much lesser known forks, some of them are probably dead (NXT Horizon, NAS, StagFlation).
So Burst, considering the "living" NXT forks, is maybe the one that stays closest to NXT, although it doesn't use Proof of Stake and implemented the Automated Transactions mechanism.
Why no activity in this community?
There is also another newer thread which may explain why this one is so quiet (new development team improving the coin).