The King Tiger was, well... somebody please tell me what they had that was just so much better than the bog-standard Tiger?
The King-Tiger was simply "...More" of the tiger - More fire power, More armor, More horse-power etc. It was actually one of the best tanks of the war, but like all German tanks it was flawed in (at least) 3 major areas -
1) Like all German tanks it had narrow tracks, which limited it's mobility.
2) It was quite unreliable.
3) by this time of the war, the German simply hadn't enough fuel. tanks were usually going into battle on less then full fuel-tanks, and got stranded without fuel in the midst of combat.
Besides, later run Panzer-IV's were tough enough to hang-tough with the T-34/85, and the M4 Shermans quite well.
A ton for a ton, the T-34 and the Panzer IV were kind of a close, with some advantages to the T-34. the real difference was the crew quality - as the Russians became better the tide tern more and more to their side.
Now, it's quite hypocritical to say the Sherman= Suckzzors, T-34/85=god's gift to armour. The later-run Sherman's got good guns, they were quick, they were capable of going through the terrain effectively, and they had... wet storage. The Sherman was a no-frills AFV that did it's job very well. If it did suck so hard, then somebody is going to have to explain the Sherman firefly, and why the Israeli's used them all the way up to 1974.
About the Sherman, I guess I over-took it a little - Early Sherman were lousy - too thin armor, week guns, gasoline engines (which tend to blow up when hit).
As the war progressed, so did the Sherman - It got better engines, better guns, thicker armor, safer Diesel engines and ammo storage etc.
But in the end, there was one cardinal rule about the Sherman and the German tanks - Most of the guns used on Sherman tanks were not powerful enough to penetrate the front armor of the German tanks it faced (mainly Panzer IV, Tiger, King-Tiger and Panther). (one of the exception was the Sherman Firefly).
But it was much faster and much more mobile - not just due to it's high speed - since it was lighter it could pass were it's heavier German counterpart couldn't.
So Shermans used their advantages to run around the German tanks and shoot their rear.
But even with this the simple truth was that for each Sherman that got behind a Panzer or a tiger, usually 4-5 other Shermans got hit (though not necessarily destroyed).
All-in-All it was a
good tank - it was however a
medium tank forced to fight
heavy, more powerful tanks
The post-war Sherman were much better - powerful engines were installed, the armor became better, as well as the guns.
And since you mentioned the Israeli use of the Shermans -
In Israel the Sherman were used as the basis for quite a few armored vehicles - including tank-ambulance, self-propelled guns, combat-engineering vehicles, Rocket launchers (and more).
As a "Tank" it was use in several variants, the last of which is the Super Sherman M-51 (which is considered one of the most power Sherman variants) with a 105mm cannon, 460hp Diesel engine, ablative armor and more.
In the Yom-Kippur war, two of these tanks were defending an outpost against 6 Egyptian T-62 tanks (the Top Russian tank of the day - the T-72 only completed it's field trials at the time). The two 25 years old Shermans managed to destroy 2 of the T-62, damage one more, and repel the attack.
The M-51 variant remained in use up to the early 1980(!), and was sold to chile (and I have no idea how long it was in service there
).