I actually run vim with a single term window within a screen session. All my window splits and tabs are handled by vim. I actually run nested vim instances within those term windows amongst other things.
In other words, screen handles persistance and the ability to reattach to an existing session. The outer vim serves as a terminal manager. The nested vim instances are used to edit code, etc.
i stopped using tmux because now all i need to do is open a terminal buffer in a new split to multiplex. i rarely used it for sessions, but use abduco[1] for that now when i find the need.
[0]: https://github.com/mhinz/neovim-remote
[1]: https://github.com/martanne/abduco