So basically while the T-34 might look good on paper with it's better armor and gun, the reality especially in 1941 was that the Panzer 3 and 4 were much more effective fighting tanks because they could be operated much more effectively and bring what they had to bear on the enemy faster which is why many T-34 were easily outflanked by German tanks due to being practically blind and having no good line of communication with their fellow tanks.
I encourage you to watch "Panzer III vs. T-34 (featuring Cheiftain)" by Millitary History Visuallized, it's a very interesting and informative video.
Yea, p3 could fight against t-34 mod.1941. Like T-70 could fight against panther (was T-70 tank crew that could destroyed 2 panther from 40 meters, start shoot to thin side armor). You have chances if could hit to rear or side armor.
But when deal comes to P4. It got the main upgrades in summer 1942 (thicked armor of turret from 30 to 50 and frontal to 80 + longer gun). Mogel H become the most perfect model from all P4. Model J in 1944 got only manual turret rotation and reduced amount of optics to become easier to produce. T-34/76 in 1943 became perfect from terms of reliability and production. While in 1944 it was fully replaced in factories by t-34/85 with much more powerfull gun and 90 mm thick turret armor (all P4 had the same 50mm turret like it was maded in 1942).
Germans could went to Moscow had only couple p4 with 75mm short gun and thin armor and tons of light tanks. While soviets had more heavier and better armored, but very unreliable tanks.
Panther was medium tank from german idea (it used as p4 replacement and must do the same work as p4), while have weight only 1.5 tons lesser than is-2 with 122mm gun and 120mm sloped armor. In fact, main problem was that P4 became outdated and p5 couldn't became good replacement. IT had problems. that couldn't be resolved, because by design decisions.
Ther were many reasons for it: from very strange style of development new tanks, when all companies have 1 task with detailed description which parts must use new tank. To have only Knipkamp, who carry on yourself all vision about future tanks in 6-th Department. Without any serious contender (from terms of political power, not technical knowledge), who can had different opinion. As result many good ideas of tanks, were not realised, because 1 company can't make the whole tank in alone. If 6-th Department made mistake in vision, this became fatal.
Such style of development was born from mistakes of 1936-1937, when multiple companies couldn't make project of medium tanks and heavy tanks even not started to develop. Army was without proper mediums and without heavies. Each company had own vision. The decision was made to create one main department which will be lead all tanks development and production and create vision of future tanks. 6-th department was born. It could fast resolve bunch of problems and gave to army medium tanks (p3) and heavy (p4). But in long distance it became weak side of tanks development.