I would contend that the tables given are far too simplistic in their analysis.

(in the following K= Kirov, A=Algerie, PE= Prinz Eugene, NO= New Orleans, C+ County class, and M= Mogami)

Full load displacements: I use this value as it is usually more accurately indicitave of a ship's true displacement than a standard displacement is. Each navy has its own version of what constitutes "standard" displacement and often during this period these were deceptive numbers.

K = 11,500
A = 11,500
PE = 12,500
C = 11,700
NO = 11,500
M = 15,200
(note all values rounded)

Year laid down and completed: This indicates about when the class was built. This compares where each was in regard to the state of the art. Later classes will have advantages from better design and lighter machinery etc.

K = 35, 38
A = 31, 32
PE = 35, 40
C = 24, 30
NO = 35, 38
M = 34, 37

Armor: Why this was left out of the original table is very unusual. This gives an indication of the amount of weight devoted to armor protection on the ship as a whole. The values given are for belt, turrets, deck in that order

K = 3", 4", 2"
A = 4.5", 3", 3"
PE = 5", 4", 3"
C = 4", 1", 1.5"
NO = 5", 8", 2.25"
M = 4", 2", 1.5"

Torpedo defenses: Of these classes all except PE and NO are about equal. Any one of the others could conceivably be sunk by a single torpedo hit and several were. NO and PE were a bit better requiring at least two or possibly three hits to sink minimum.

Range: This gives some indication of the fuel load and machinery effeciency. It is a better indicator of how good the plant on the ship was than top speed.

K = 3,000 / 18
A = 5,000 / 15
PE =
C = 13,000 / 12
NO = 10,000 / 15
M = 8,200 / 14

As one can see from this list combined with the previous one, the Kirov is definitely a heavy cruiser even if her main battery is a bit smaller than her contemporaries.
Of the group, the PE and NO classes are the best protected with the NO having an advantage in steaming range and firepower over the PE.
The Japanese Mogami class really comes off badly. At over 15,000 tons she ships just one more main gun than a New Orleans and two more than a Prinz Eugene, has less armor and less steaming range than the American ship.
The French Algerie is not too bad given her age. But, the ship has a very short range, a defect shared by the Kirov. But, the Russians apparently were not building true "blue water" cruisers so this defect is not as important in the Russian design. For the French, the short range is only acceptable for Mediterrainian operations.
The British County is an early commer to the race. Some exception has to be made for their age. On the other hand, they are hands down the best cruising ships, a very important design concern for the Royal Navy. They have the longest range and are very good sea boats. Their glaring deficency is poor armor protection, a trait shared with the Mogami's and less excusable in the later given their massive displacement.

On the whole, the line up now appears:

New Orleans
Prinz Eugene
County Class
Algerie
Kirov
Mogami