Are there any issues or special settings to be able to have both a joystick and an Xbox controller plugged into FSX-SE and use simultaneously?

I have always only used the Logitech Extreme 3D Pro joystick but I have just added Chase Plane and from what I am reading it is recommended to use the Xbox Controller in order to have access to additional buttons and movements for Chase Plane Assignments.

Not official answer, just personal opinion. Might be wrong, but I can not imagine any button or movement that is not possible to assign to your existing controllers (joy+keyboard). Yes, Xbox controller would add few more free axis+buttons to use with camera controls, that can be handy if you wish to create sim videos and etc. But otherwise you can use keyboard for many controls.
If this helps you, here is my setup - F1 to F11 keys used for different cockpit views (I don't need their default assignments as I have yoke + throttles, same as you do). Notice that I don't use F12 as this is used by many other programs that I run in background. Numpad keys for moving camera up and down + some more (again - no need of default assign. because I have ChasePlane), Keyboard arrow keys for moving camera left, right, fwd and backwd (just make sure you remove default settings for these in simulator) and finally yokes hat-switch for panning around.
I would love to hear any suggestions regarding this.  

PS. Forgot to add - i use one of my Saitek Cessna yoke horizontal switches for selecting next/previous view in the category, but you can assign this to any 2 of your joysticks buttons.