I have used both. E200 one stop push works better at ISO 320, which matches the Kodak data sheet recommendations. Beyond the data sheets, I have used E200 extensively out to 4 2/3 stops push, though it is not linear, shifts somewhat bluer, and requires exposure compensation.
I have used a few rolls of Fuji 400X, including pushing a couple stops. The push performance is a bit more linear than Kodak E200, though some exposure compensation helps. The colour balance is not as favorable to skin tones, with the E200 seeming more natural, compared to 400X which seems more greenish. Fuji 400X is also higher contrast than Kodak E200. The real advantage I think Fuji 400X has over Kodak E200 is when used beyond ISO 800 (3 stops on E200, and one stop on 400X).
Both films have their uses. If you shot both at the same time, under the same lighting conditions, then the differences become quite obvious. I have done a corporate portrait session that way, and the E200 shots seemed warmer and more natural. When I last shot a jazz concert with 400X, the results were very appropriate for stage lighting; I would likely use it again under those conditions.
Ciao!
Gordon Moat Photography