Nakajimas were used by IJA. Mitsubishi were used by IJN. How different were they: Armaments, Speed and Maneuverability, their ability to fight against their adversaries and such.
Remarkably similar, reflecting the philosophies of the Japanese military and her unique requirements.
The Mitsubishi A5M and Nakajima Ki-27 were very similar in performance, the army fighter being a little faster and the Mitsubishi having greater range (something the Japanese Navy aimed at more than any other force in the world). Both may be seen as interim fighters. The Japanese began their aviation industry by importing a huge selection of aircraft, then moving to licence production of European types, then 'importing' foreign, mostly German designers to create new planes, and finally with these aircraft the Japanese were seeking to build modern fighters with all-metal construction and other modern features.
Both companies also developed aero engines. As in many nations (USSR, Germany), these were evolved from original US designs, but by 1944 very much separated from the 1920s originals.
The next generation of fighter was the A6M Zero and the Ki-43 Hayabusa. These represented proper, state-of-the-art fighters and it is no coincidence Japan embarked on war with the West soon after their introduction. Both were very light by Western standards, the A6M being the better and more balanced design. The Ki-43 was light mainly to gain maximum maneuverability, as this is what Japanese pilots prized (to their long-term disadvantage). It is a measure of their similarity that Allied pilots generally identified both these aircraft as 'Zeroes' and were often unaware when Ki-43s came to replace A6Ms on certain fronts. The A6M had more development potential, being larger, but unfortunately for Japan these aircraft were both required to soldier on long after they were obsolete.
At this point it is worth mentioning the Ki-44 'Tojo' and J2M 'Jack'. Both were designed for interception. This requirement was identified as the Japanese considered defending their empire, rather than capturing it. It is probably no coincidence that both services decided they wanted similar fighters at a similar time, intense rivals they were. Both planes sacrificed maneuverability for rapid climb and armament. The Ki-44 was quite successful, only ever supplementing the Ki-43, but the J2M took years to develop and never really worked very well, in part due to engine problems (see below).
Developing the next generation of fighter proved an almost impossible challenge for the Japanese. Many of these issues stemmed from engines. The 1000hp-class radials that powered the earlier planes were cutting edge in the late 1930s. But learning how to build a modern engine did not help the Japanese develop the wealth of industrial skills necessary to develop the next generation. Their 2000-hp class engines were almost all failures, or took a very long time to gestate. Their metallurgy, electronics, and other background industrial processes prevented them from getting a reliable, lightweight engine or developing other needed technologies like turbocharging. Japanese fuel was low octane, another big problem.
The late-war aircraft Japan developed were potentially excellent. The Ki-84 'Frank' was just as good as a Mustang or Spitfire. But while able to build an excellent airframe, Nakajima could do little about the mediocre training of pilots, the poor maintenance of increasingly service-intensive machines, the lack of self-sealing fuel tanks, or the bad fuel. Mitsubishi never really got its Zero successor into production. Incidentally, the quoted figures for Japanese fighter performance are often based on US tests with high-octane fuel, and the average Japanese pilot could never achieve the same results.
So, both companies' aircraft had similar strengths and this required Allied pilots to face them in the same way, using hit-and-run tactics and maneuvering in the vertical plane (as the light IJN/IJAAF fighters could turn inside anything in the Allied inventory). Caught low down or at low speed, even Corsairs and Spitfires were vulnerable to a Ki-43. But keeping up their speed, Allied pilots could engage and break off at will. By the time the Japanese had comparable fighters, there was a huge disparity in pilot skill and reliability.