A better question would be in general in all nations' armor corps, but I am very fascinated with German armor of ww2.
So we have an armor battalion. Let's say the composition are panzer 4's, Panthers and tigers. Were heavily armored tanks like the tiger were given to more experienced crewman? Was there a hierarchy of tanks, in which if the crew was promoted, was given a better tank?
Generally, this was not the case, but if a battalion entirely converted from, say, Panzer III, to Panzer IV, to Panther, over time, a sort of "upgrading" could occur, but not exactly under the criteria you specified.
A German Panzer Division late in the war was theoretically supposed to have one battalion of Panzer IV, and one battalion of Panthers. If a crew ever changed battalions, they could potentially get a "better" tank (the Panther), but I don't ever recall crews being assigned "better" tanks based on experience. Retraining many crews while the division was in action would sap manpower. Once a crew was trained and assigned to a tank, they generally stayed with that same tank type unless the whole battalion converted to a better type as described above, or they were transfered to a new battalion.
Mixed panzer battalions as you describe did exist in the German Army. A 1942 German panzer division had three regiments, with two light companies (Panzer II and III) and one medium company (Panzer III and IV)
Early in the war, each of eight platoons in a schwere panzerabteiliungen (Heavy Panzer Battalion) was made up of two Tiger tanks and two light Panzer III tanks with 75 mm howitzers to protect the Tigers from infantry attacks. Each company's (there were two companies per battalion) commander would have a Tiger, and battalion command had two Tigers, for a total of 16 Panzer III and 20 Tigers. Later in the war, the Panzer III's were dropped and the battalion had all Tigers, for a total of 45 Tigers.
Sources: Wolfgang Schneider Tigers in Combat I and II
achtungpanzer.com "Structure and Strength"
Spelling edit: panzerabteilung*