OK the variance between the Yaks depends upon exactly which model you take for comparison.
Full Name: Yakovlev Yak-1 and Yak-3
Variants: Yak-1M and -3
Type: Single-seat fighter
Country of Origin: USSR
Manufacturer: Yakovlev
First Flight: (Yak-1M) 1942; (Yak-3) Spring 1943
Engine(s): (Yak-1M) one 1,260 hp Klimov VK-105PF vee-12 liquid-cooled; (Yak-3) 1,225 hp VK-105PF-2; (final series) 1,650 hp VK-107A
Wingspan: 30 ft 2.25 in (9.20 m)
Length: 27 ft 10.25 in (8.50 m)
Height: 7 ft 10 in (2.39 m)
Weights: Empty: (VK-105) 4,960 lb (2,250 kg); Loaded: (VK-105) 5,864 lb (2,660 kg)
Maximum Speed: (VK-105) 404 mph (650 km/h); (VK-107) 447 mph (720 km/h)
Initial Climb: (VK-105) 4,265 ft (1,300 m)/min
Service Ceiling: (VK-105) 35,450 ft (10,800 m)
Range: (VK-105) 506 miles (815 km
Armament: One 20 mm ShVAK, with 120 rounds, and two 0.5 in (12.7 mm) UBS machine guns, each with 250 rounds
As you can see the later models were equipped with the same 1600HP Klimov as the Yak-9's.
It's interesting to note that the Yak 3 was actually developed after the Yak-9 series, the 9 being a descendant of the 7 series tandem trainer which was developed as a result of research into a heavy fighter variant which was actually first produced as the Yakovlev I-27 in 1939 and presented alongside the I-26 in 1940 as the UTI26. Yakovlev actually presented FOUR aircraft prototypes to Stalin at the same time including the I-26, UTI-26 (I-27), I-28, and I-30.
Another side point is that the Yak-9U was also equipped with hardpoints for two bombs of 100kg each, something our U's cannot do.