The 76MM gun on Shermans could not easily take out Tigers or Panthers. Another tidbit on this, is it is the same gun used on on the M10 and M18. but the tank units did not get the APCR round that made it more effective, those went to only the tank destroyer units(at least early on).
It was better then the Short 75, and great agaist the Panzer 3 and 4 but would still fail to penatrate the frontal armor on a Panther or tiger even at ridiculusly close range.
Another thing about the 76 gun shermans is they did not go into action untill late 44 I think.
One advantage the Sherman had that no one has brought up is it had a stabilized gun, and when it was working would allow the sherman to move and shoot at the same time.
Belton y Cooper talks about that in his book Death Traps : The Survival of an American Armored Division in World War II
Link (Great book if you want to know how much of a nightmare it was to be a US tanker in Europe.)
The Sherman could hold its own against Panzer 3 and 4s, its gun could kill the both without to much trouble. Its armor was ok against the 50mm gun on the 3. The long 75 on the 4 would kill it the Sherman with ease.
The Sherman had really narrow tracks making it less mobile over mud and snow then even the Tiger. A big problem.
Heck even the 90MM gun on the M36 and M26 tanks, still had some trouble killing Tigers and panthers, the gun on both the Tiger and panther could take out an M36(way further for the M36 since it had light armor) or M26 tank further then the 90MM could take them.
The M26 was close to a Panther in armor and a pretty good tank over all. In the book I reference about they talk about a special version with a really long 90MM gun, look wacky and had to have big springs on the top of the turret to counter the weight, they ended up cutting the front Armor off a Panther and adding it to the front of the M26 to help keep it alive. He includes pictures.