I'll do a Roel: http://www.fun-online.sk/forum/viewtopic.php?t=1205 Or do you mean an 'AFV-but-not-a-tank' vs 'AFV-but-not-a-tank' battle?
If we´re not thinking tanks. The RNAS used armoured cars as early as 1914, in Belgium against German cavalry patrols and infantry. I believe, however, that the use of armoured cars was pretty one-sided until much later in the war.
The Belgians first used adapted Minerva touring cars with armour and mg armament to check German cavalry in 1914. I think that was the first use of AFVs in battle. The first tank Vs tank was (from memory) near Arras in (?)1917. German A7Vs and captured British tanks against male and female mk IV British tanks. The honours were fairly mixed. Someone help me out with accurate details huh?!
French army used this armoured car in 1906. Was also exported to Russia, the same year. Reportedly used by both nations in the opening stages of WW1.