I’m gonna compare the P-63A-10 with P-51D-5 in order to explain you why they belong in the same BR:
Well I have compared this 2 fighter planes and I don’t see how P-63A-10 is BR IV and P-51D-5 is BR III.
P-63A-10 is low altitude fighter while P-51D-5 is high altitude but as performance wise they are very similar and yet played very differently. P-51D-5 is good at Hight altitudes and better air to air capabilities since it has 6 machine guns compared to P-63A-10 4 machine guns the P-63A-10 compensates with 37 mm cannon but since its a slow cannon you can use it only against ground targets or slow planes which will make it absolutely useless against faster planes.
When it comes to bombs they are also very balanced. Now lets compare it with the starting German and Japanese BR IV fighters:
BF 109 G-6:
Well as you can see here the firepower is even bigger considering it has 1x20 mm auto cannons and 2 better machine guns and the cannons are fast. When it comes to performance they have very similar turn rate but in every other aspect G-6 is better there is also 1 more factor that makes the G-6 better dog fighter and this is the controls the G-6 is much more stable in the dog fights since P-63 has similar to FW controls but better however still is one of those sensitive planes. When it comes to bomb load they are very similar 4x60 kg cover better area 1x250kg is better against big targets and they are in the middle that is the best place for bombs for planes.
So G -6 is better plane hands down. However G-6 is high altitude fighter very similar to P-51D-5 but better do to better fire power and specially in longer fights with P-51D-5 the G-6 will come on top. If you are P-51D-5 player avoid longer engagements with this plane. Also trading shots is not good option do to auto cannons. Best way to engage him is from higher altitude but if he is on your tail well that’s bad like very bad… however the good thing is if you are on his tail you have good chances since everything he can do you can do also. Without one flaps trick that is very hard to pull up.
Ki-61-II Otsu Kai:
The Ki-61-II Otsu Kai is low altitude fighter very similar to P-63A-10 has a bit less bomb load but it definitely covers it with the most insane firepower having 400 rounds in its auto - cannons means he is up for a trade in shots he is up for a spam he is up for 2 vs 1 battles he has enough ammo to put 2 planes down. In a dog fight as performance wise the P-63A-10 and Ki-61-II are very similar but do to the sensitive controls is much harder for P-63A-10 to dogfight and do to the bad armament of P-63A-10 with its slow velocity 37 mm cannon and only 4 mgs trading shots is not a good option unless you get some lucky 37 mm hit. Overall the Otsu is better plane. Specially if you lower its speed below 600 and put the flaps you will win the dog fight.
So i think its wise to put P-63A-10 to BR III since its biggest problem are fast fighters and against this super fast Jet planes I don’t see how its slow velocity 37 mm cannon and 4 mgs will be enough to engage any jet fighter. Specially if the Jetfighter refuses to get in a dog fight and just zooming you all the time. And even in war thunder P-63A-10 is with battle rating 4.0 Similar to P - 51D-5 that also is 4.0 and majority of Jet fighters are with battle rating 7+ … and here P-63A-10 is performing worse then in war thunder. So in war thunder the good dogfighters planes are very good against bad players and very bad against good players since good players wont dog fight you and if the dogfighter don’t have good fire power and good speed you cant survive the booming and zooming spam. And if P-63A-10 had more fire power would be able to fight such planes since the speed is not that bad but just the 4 mgs and the low velocity cannon wont be able to do enough damage to the jet fighter if he misses you and he will probably fly away and zoom you again. While the Ki -61 and G-6 have enough fire power at least to punish the jet if he misses. However the Ki is on the slow side so it may have some troubles the G-6 will be better since is high altitude fighter and will have the best chances against jets from this 4 planes.