Although not the same player explicitly, I wouldn't say that Muntari and Tiote could play together. I'd thus pick Tiote over him (ignoring his bit part in a Champions League win).
My team would be:
Gordon (Sunderland), Onouha (Sunderland), Enrique (Newcastle), Coloccini (Newcastle), Williamson (Newcastle), Sessegnon (Sunderland), Ben Arfa (Newcastle), Tiote (Newcastle), Barton (Newcastle), Carroll (Newcastle), Gyan (Sunderland).
The midfield is very difficult, because Richardson is rather good and Nolan shouldn't really miss out. They'd both definitely make the seven man bench:
Harper (Newcastle), Mensah (Sunderland), Elmohamady (Sunderland), Nolan (Newcastle), Richardson (Sunderland), Muntari (Sunderland), Welbeck (Sunderland).
There'd be no place for players such as Cattermole (simply not as good as Tiote), Zenden and Bramble, nor for Ameobi (although naturally he'd be part of the squad due to his status as the irremovable object), Simpson, Smith and others. To complete a 25-man squad, I'd include:
Krul (Newcastle), Bardsley (Sunderland), Turner (Sunderland), S. Taylor (Newcastle), Gutierrez (Newcastle), Ireland*/Guthrie (Newcastle), Ameobi (Newcastle).
* Assuming he signs while this thread is still active, if not include Danny Guthrie.
Unintentionally, that gives both teams 9 of the first 18, and Newcastle 5 of the 7 further reserves. Sunderland do have some depth, but much of it hasn't done well in England thus far (Riveros, Angeleri), so when it came to the 19-25 spots it made sense to go for those with a track record.