The weight of fire for the (3xB-20) Yak-3P was 3.25 kg per second.
A very few saw action by war's end but most of the 596 built were post-war.
One B-20 cannon was unsynchronized so you'd expect it to beat the made in Moscow La-7 with it's 3 synchronized B-20s. It put out 3.4 kg. Both were enough to be a welcome improvement. (Most La-7s had only 2 ShVAK 20-mm cannons like the La-5)
Maybe the difference was in the engine they had to synchronize with.
The Yak-9UT is the one with the twin B-20s and a hub NS-37 for a 6 kg weight of fire per second. It was only in time for the Berlin assault (many of the 282 built participated). Careful of that high velocity recoil!

The VK-107A powered Yak-3 did not enter service in WW2. Too many problems and the -3 airframe was not as suited for this enging as was the Yak-9U.
The Yak-3's roll rate equalled that of any Fw-190 and its turning circle was smaller than any contemporary fighter in the VVS.
The Yak-3P was the definitive production model of WW2. Its armament was three B-20s (lightweight and fast firing 20mm canons. The Yak-3 and the Yak-3P's performance was nearly identical. Both shared the same VK-105PF2 engine producing 1320hp at combat power. The following is typical performance of the Yak-3:
352mph/SL. 401mph/14,104ft. Climb: 4450fpm/SL and it could climb to 16,400ft in 4.5min. The PROTOTYPE could climb to 5K in 4.1min. and reach a top speed of 404mph/14,104ft. and had an initial climb of 5100fpm.
It must be noted that production problems from time to time did vary these figures, but most were as stated above.
The Yak-3P was utilized in 1945 and did not see action against Germany. Two squadrons became operational against Japan from August 8 on. And they performed excellently against such aircraft as the Ki.61 Tony and Ki.84 Frank.

The new built Yak-3Ms with the Allison V-1710 engine makes for a great flying, very dependable little warbird.The airframe is built like a Mack truck (very strong) and contrary to what you may have heard, the airplane is easily managed by almost anyone, provided that anyone has some good quality tail dragger experience. I have a Yak-3M and love it.

Terminal dive was said to be 578 mph. Red-line may be much less.

This is the one the Luftwaffe was warned about! It evolved from the light Yak-1B so it was more vulnerable than other types but it added a 3rd gun vs 2 for most Yaks and Lavochkins.
It was the first hot Yak, more speed for the same power. It's wingspan was shortened giving it a better roll rate than an Fw 190A some say. This also made the landing hot (fast). It took over top cover duties from the La-5FN and was numerically the most important Soviet fighter for the last year of the war. The French unit mentioned above, could have chosen any Allied fighter but this was their pick to finish the war in. Sorry Spitfire, sorry Tempest and Mustang ...etc.
I believe the Yak-9U was the one powered by the VK-107A before the end of the war. The Yak-3 did also get this engine but it was effectively postwar. Thus, it suffered in negative-g initial dives like all VK-105 powered Yaks during the war.

Weight of fire / sec. salvo = 2.72kg
Climb to 5km = 4.1 min.
360 turn = under 19 sec.