The Thing is, 75mm Equipped Shermans were considered to be doing just fine in 1944, at least by the Americans.
The US had been understandably hesitant about introducing 76mm Shermans, given their weaker HE rounds. Given that Shermans literally spent 90% of their time engaging targets that should be considered soft (trenches, AT guns, infantry ect), this is understandable. Coupled with the fact that most of the armour they encountered was still perfectly engagable at realistic combat ranges (Pz4s still made up the bulk of the tanks used in Normandy by Panzer Divisions) Then it is pretty obvious as to why the 76mm Shermans took a while to come into widespread service, when they could of been easily introduced far earlier (prototypes were ready in 1942 IRRC)
What's more, Panthers did pretty poorly in Normandy, owing to the terrain and rather weak side armour for a tank of that size and profile. Frequently authors such as Zaloga or Buckely have paraphrased German Tank commanders preferring the Pz4 in the Bocage environment because of its much more practical profile, as well as not suffering glaring design or reliability faults. (Having a turret that could not traverse over an incline due to a weak turret motor is just one of many of the glaring faults of the Panther) Furthermore its been pretty much proven by this point that the panther had significant problems in its layout, with the gunner not having an observation periscope being one of the more glaring faults. This would explain why Sherman's often managed to spot and engage targets sooner than their German equivalents, as they had by comparison much better situational awareness through the addition of more periscopes.
It was also more readily apparent that the Panthers strong front armour wasn't exactly that great in the Bocage, given that over 60% of recorded hits on vehicles in the Normandy campaign were struck on the side. Given the Panthers shoddy ammunition storage placement and tendency to catch fire rather easily coupled with paper thin side armour, they didn't do too well after taking hits from the side.
Now, this isn't to say the 76mm Sherman was bad, in fact it was a very useful upgrade which extended the service life of the Sherman considerably, and gave it even more punching power against the occasional threat that might of actually been a problem. Given how rare the Tiger 1 was for the Americans to encounter however, one could argue that the point is moot. (especially given that 75mm Shermans could easily penetrate the front of the Tiger within 300 yards with the APC ammunition, let alone what the 76 could do without HVAP)
Its somewhat fortunate that the British were the ones facing the majority of the armour in Normandy, which justified the usage of the Firefly in widespread service, despite its faults. Certainly, the track record of the German AFV's was not because of their design or any qualitative advantage, but merely due to the fact they were on the defensive, often in concealed positions and thus able to achieve the all important first shot. Buckley does make the very important point that German armour encountered the same difficulties that the Allies did on the offensive, not to mention taking similar loss ratios, as demonstrated during many of the armoured counter attacks the Germans made, which were defeated rather easily by the combination of infantry, AT guns, Allied tanks and artillery support. Again, the point is that attacking with tanks is always going to be costly, especially when facing a competent opponent, regardless of what sort of tanks you use.
The overall point is I think, is that Allied armour has been underestimated in its capabilities for some time, which is largely a result of a number of factors, one of which is the notion that German armour was always qualitatively superior, a notion that is utterly false. Sherman's were one of the safest vehicles to be in, especially once stricter methods of ammunition storage and wet ammo bins were installed. Much of the Sherman bashing you see on TV or in video games is entirely unjustified and categorically false.
Sherman's should do just fine against the German tanks, let alone the more specialised vehicles such as the Firefly being considered.