It won't be like rust. From what I understand 24 people at most in a map 4x the size of Fallout 4's which gives us approximately 40km^2 to play about in. Dying doesn't make you lose anything from what I have read and you can respawn easily enough. While there will be PVP aspects to the game you won't be punished for dying
It's not going to be anything like ESO, ESO is an MMORPG where as Fallout 76 is just going to be a multiplayer fallout game. It's radically different from an MMORPG. Also ESO is made by Zenimax Online and not by Bethesda, they don't really have all that much to do with ESO.
I'm personally looking forward to Fallout 76 after watching the noclip documentary on Fallout 76 and as much stuff as I can from E3 involving Todd Howard. It's a game that they went to get right at BGS, they have plenty of plans to keep it alive for a long time and they're looking to find a balance so PVP isn't too much of an issue if you do get killed. I am looking forward to being able to explore WV with friends