I'd probably take the I-16, but not having flown either, I can't really say which one would win.
Heres my take on it, this being the FAF 239 VS the SAF I-16s. The 239 was not necessarily the better aircraft, or, better by much. The FAF pilots were far superior, as were the tactics they used. Remember in our pacific war we avoided turn fighting the zeros like a plague. Well so did the Finns in their 239s vs the Ratas. The I-16 had compression issues in a hot dive. This may not mean that much in a game like AH, where there is always a faster fighter that can dive with you and out run you. But in actual war this is a huge advantage. Even in the game the runstangs and FW-run90s make full use of their "dive and run" abilities. In real life such an edge means life. To be able to break off at will is a huge advantage. At this point its necessary to say that the FAF had one of the most aggressive Doctrines of the war. They almost always attacked regardless of the numerical disadvantage.
As was the longer legs of the 239s. BTW the FAF had a small number of I-16s and thought well of them. They liked the 239s better but still thought well of the Ratas.
As far as guns go I'd have to give the edge to the 239s. They all had a 4th Browning 0.50 installed and 4 Yanks 0.50s is a premium early war package I believe. Even after the Ratas were given heavier guns I dont think the Soviets guns could compare with the 0.50s, "which btw the Finns liked so much they copied for their own use". It didn't hurt that the Finns were terrific shooters either.
Add to all this the Soviets didn't personally like flying high. Dont ask me why. Either they just didn't like it, liked flying in the clouds, or just weren't allowed to. But when against any Yank jabo, when you run into them and they have a lot of Alt. on you?, your probably going to have a problem in the energy fight that follows. That is if the enemy is disciplined and stays within his performance envelope. The P-40s of The Flying Tigers were another example. They used their superior roll rates, better dive abilities, and longer range of their 0.50s to max advantage.
Also dont forget the Rata faced JAAF in 1939 at the Nomonhan Incident and gave a good account of itself. Its hard to get an accurate picture of the large air war that accompanied that battle, both nations very secretive and Japan destroyed almost all its military records in 1945, but the Soviets ended up controlling the air and the JAAF was seriously depleted from losses. No doubt there was more Soviet aviation talent at Nomonhan then on the Finnish front just as there was more army talent "Zhukov" assigned to defend the vital Siberian resources.
So my guess would be the better Pilot would win, one who used his planes strengths to full advantage. I think the Brewster vs I-16 Rata could be one of the great match ups of the game.