[loggedUser isStaff]
seems to be an NSNumber / Boolean object yet you are trying to compare it to an NSString. Booleans and NSNUmbers do not have an isEqualToString method.
If you want to compare whether the user isStaff, you should try:
if ([[loggedUser isStaff] boolValue])
{
[self performSegueWithIdentifier:@"staffLogin" sender:self];
}
else{
[self performSegueWithIdentifier:@"userLogin" sender:self];
}