The P-40 didn't climb well, but exactly how badly it climbed depended on the variant. and the power setting. You are referring to a D or E used at lower rated takeoff or military power. The Tomahawk (B, C) had a 2,800 fpm + initial climb rate. The K had almost a 3,000 fpm rate as well if climbing at higher power settings they used in the field up to about 12,000 ft. The P-40L-10 climbed at 3,300 fpm according to "The Curtiss Hawks", Wolverine Press, 1972 - P.234 and Carl Molesworth's, "Snub nosed Kittyhawks and Warhawks" (2013), P. 32
P-40F was the same as the L when they were stripped down for fighter combat, as they usually were in the MTO. But climbing performance wasn't the only measure of a fighter.
Without any doubt we could debate stats all day long which would be quite pointless. I'm not talking about performance stats, I'm talking about the operational history. The P-39 and P-40 were used roughly in the same quantities in the Pacific, in fact there were
more P-39s deployed during several key battles such as at Guadalcanal (probably because on paper they looked like they would be better) and yet P-39 units claimed less than half as many victories as P-40 equipped units did (288 for P-39s vs 660 for P-40s) suffered more losses, and had a lower morale. If you include the ANZAC P-40 units that's another 248 victories. So I would say P-40s did a lot better there.
In the CBI the ratio was 5 claims for P-39 equipped units vs. 973 for P-40 units (only counting US and not Chinese units here). I don't think that many P-39s were used in the CBI though.
In the MTO, where P-39s were available in some numbers and for a comparatively long time, US units equipped with that fighter only claimed 25 victories, vs. 592 for P-40 equipped units. If you add Commonwealth units equipped with P-40s that goes up to 1042.
The total number of victory claims for US P-40 units in WW2 was 2225, making it 5th for all US fighter types, abvoe the F43U and the F4F. The total for the P-39 was 320.5, making it 10th, just above the SBD Dauntless.
Source
There was also only one pilot who made Ace in the US military who flew P-39s, vs. at least 86 for the P-40. Not counting another 46 British Commonwealth pilots who became Ace while flying the P-40.
Now of course we know overclaiming was a thing, and I'm sure actual victories were far lower than 2225, but there is no reason I can think of to assume that that units equipped with P-40s, recruited from the same pool of pilots as the units equipped with the P-39s, would have been overclaiming at a higher rate.
In the Med, the P-39 was considered so ineffective in combat that they were relegated for a long time to 'Coastal Patrol' operations. At the same time the P-40 equipped units were bearing the brunt of combat with the Luftwaffe and Regia Aeronautica. Only later when improved models became available were P-39s used for CAS and bombing strikes, though they were limited in this role by their short range.
The P-39 proved it's merit in Russian hands, but with the Western Allies it was a major disappointment and when it came time to face the enemy, they failed in the litmus test, underperforming, whereas the P-40 tended to overperform vs. expectations, paticularly in the mid-war period. P-39s were tricky to fly and accidents also cost the lives of some very talented pilots flying for the Italian Co-Belligerent Air Force and the Free French. The Soviets may have been uniquely qualified to use it, or maybe the Americans just didn't give it the propepr work up it needed. The bott