Does the game run any different? No. It's the same thing since MW1 in 2007.
It only cost me $10 to upgrade from 360s copy to X1 @ Gamestop so i figured it was worth it. Graphically it looks slightly sharper and you can definitely notice right away it's an improvement.
Does it feel next gen? No b/c again its the same recycled junk! Sure it looks great but I got bored of this after 5 online sessions.
I will admit it is probably one of the better launch title releases out there. Already tons of players online to support the community so no problems finding games. Servers are lightning fast no hic-ups, lag, time-outs or lost connections after a few hours. It really runs as smooth as it always has which is a good sign. (COUGH BF4 COUGH!)