The main difference is the original flora respawn fix was not tied to the cell respawn timer and the new one is. The new one also fixes some additional and somewhat unrelated minor bugs (listed on the mod's Nexus page) and does not cause save game bloat or increased memory usage. The original flora respawn fix causes a very small amount of save game bloat and memory usage since the save remembers each time you pick a plant. But the amount is very small, so unless you play the character a very long time and pick a ton of plants all the time, you may not notice. The original also seems to require fewer compatibility patches.
I still use the original flora respawn fix. I prefer it since it lets flora respawn without needing the cell to reset. I hate the way Bethesda designed cells not to reset unless the player stays out of the cell for X days. It is annoying that the respawn timer resets every time the player enters the cell, because I find my characters avoiding cells or waiting in inns for ten days just so places will respawn, which is totally unimmersive. In the past (before flora respawn fix when I was playing in console), the main reason I would want a cell to respawn is so plants would grow back. Now I don't have to worry about that.
With the original respawn fix, cell reset is irrelevant to whether plants respawn. Instead, plants respawn on their own timer and it does not matter if the player is in the cell, the plants will respawn. I like this approach very much since plants will grow back even if I am there, which is immersive. Plants should not stop growing merely because the PC passed by at any time less than 10 days ago.
The author of the new respawn fix did not like this mechanic since it leads to the possibility that a plant might respawn while you are watching it if you happen to stare at it at the exact moment the timer runs out, and he also wanted to eliminate the minor bloat/memory issues and fix a few other minor bugs.
Either one is a viable option. If your like me and really value plants respawning even if the cell doesn't, then the original is probably the one to pick. Otherwise, the new one seems like a good choice.