To adress the first part of the question in the beginning of the war the soviets had many planes that were out of date many squadrons still used I-15's, (not to say other powers did not use bi-planes, the US navy, the royal navy the luftwaffle and the RAF still used bi-planes into the early years of the war although in a much smaller way then the Red Airforce) however in the spanish civil war and in kaklin gol the soviet I-16's were equal and often better then the enemy planes such as the bf-109 A's, the assorted german bi-planes and the KI-21. In the first days of operation Barbarossa, much of the Soviet Airforce was destroyed on the ground, the few that got into the air had major difficulty getting close enough to the new bf-109 E-F's to get any kills however the much lower airspeeds of the i-15s and Po-2s meant that many german pilots had difficulty killing the Soviet pilots. As the war continued new soviet designs were put into production such as the La-5 and the yak 1,3,7 and 9s were able to compete with the german Fw 190s and the later bf-109 Fs, additionaly the western allies began sending planes under the lendlease agreement such as spitfires, p40s, p39s and A-20s which unfortunatly the soviet tactics were not very good for many (however the soviets loved the p39s and A-20s). Near the end of the war new designs were produced by the Soviets such as the La-7 and 9 these planes while not seeing much fighting were very powerful.

To answer the second part of your question, the Soviet pilots were trained as well and later in the war much better than the german pilots. Additionaly the planes these pilots flew were often equal to the german planes and in the many cases where they were not they would be used in diffrent ways (for instance the Po-2 being used as a night bomber to great effect and the I-15s being used very well in the caucasus mountains as the german fighters could not manuver through the valleys as well as the bi-planes). However in the early years of the war the soviet airforce was orginised very badly leading to situations where bombers would fly without escort and fighters would be sent to attack convoys (this was slowly fixed in 1942 - 43). I also feel it is useful to point out that the soviets were the only ones alowing women to serve on the front lines including in the air force such as the famous 'Night Witches' they were a part of three women only aviation regiments however women were allowed in all regements such as Anna Egorova whom was the first female pilot to fly the IL2.

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Finally the german aces that had many kills the 100+ kills they would get were mostly from the spanish civil war and other early conficts where their aircraft were far better aganst pilot that had only learned to take off and land these pilots while still incredibly skilled could not be replaced later in the war as fuel shortages hit the luftwaffe and training was the first thing that was done less of