Various circumstances of defense and attack preparations
General rule for WW2 operations was that attacking force suffers most casualties breaking trough the defenders fortifications and lines. Of course, the better these preparations are (and harder the terrain) you could expect heavier initial casualties. Defenders on the other hand suffer most casualties from initial artillery and aerial bombardment, and latter if the lines are breached trying to counter-attack or worse being surrounded, cut-off, routed and destroyed. Let's see how this apply in given examples.
For Operation Epsom, it must be noted that German defensive preparations were not that great, because they didn't have time to build elaborate fortifications inland (their efforts before the Normandy landings were concentrated mostly on Atlantic Wall) . Also, natural obstacles (bocage above everything else) were not that great in this part of Normandy. However, British on their part had problems of their own. Air support was sporadic due to the bad weather. British artillery never had firepower of let's say Soviets or even Americans. In fact, British artillery doctrine believed in "neutralization" (suppression) rather then outright destruction of enemy forces. As a consequence of this flaw (which will repeat itself in subsequent battles), British failed to achieve decisive breakthrough. Instead, they were pushing slowly forward with Germans being able to reorganize themselves after each British advance. And as a consequence of not being able to decisively breach German defenses, British suffered steady casualties. Germans on the other hand made few errors on their own, with their failed counter-attacks often running into British anti-tank fire and dug-in positions. Main German error was that they were still deluding themselves they could organize armored thrusts that would decisively turn battle in their favor. Overall, they allowed themselves to be drawn into battle of attrition which strategically was better suited for Allies.
For Operation Jupiter, nothing really changed, except that British enjoyed better air support. German casualties (given at more than 6000) are disputed. It is possible that they contain losses from both Epsom and Jupiter. Again, no decisive breakthrough was achieved, but again Germans didn't have continuous defensive line and were sucked into pattern of attack and counter-attack.
Operation Goodwood differed from previous in two important aspects: first, British organized powerful air strikes at the beginning of the operation (including heavy bombers) and second, Germans were able to better prepare themselves, creating continuous defense line and defense in depth with liberal use of minefields. This coupled with positions in Caen itself (buildings used as fortification) helped them to reduce initial casualties. There were fewer German counter-attacks in this battle, possibly because of attrition of their armored forces. On the other hand, British actually relied more on tanks in Goodwood, because their infantry forces already suffered a lot, and manpower shortage after 5 years of war was felt in Britain. As a consequence, losses of armored vehicles were skewed in German favor. However, German forces were already starting to crack, and British did manage to surround and compel to surrender certain units.
Finally, we have Operation Bluecoat. This operation is often forgotten in historiography, because it mainly served to pin-down German forces and support much better known Operation Cobra. Again, it was preceded with heavy air strikes, however they were not that effective because of poor visibility. German defenses were of various quality, sometimes British attacked well-prepared fortifications supported by minefields and sometimes they managed to find gaps in German lines which were crumbling because of constant fighting and Cobra unfolding to the west. Main objective, to pin down German armor, was partially successful . Germans did manage to organize Operation Lüttich, but this failed for various reasons (attrition of German armor in previous months, Allied air superiority, low morale etc ...) . As for casualties, they are hard to discern for this operation, especially on German side because at this point Germans were nearing collapse and records of losses are often intertwined with losses during Cobra and subsequent retreat. For the British, pattern of heavy losses attacking well-defended positions repeats itself, and again we have numerous losses of tanks from anti-tank fire . German did lose some of their tanks in small scale counter-attacks to restore their lines, but overall casualty ratio was again in their favor.
To sum things up, British strategy in Normandy devolved into war of attrition, intentionally or not. They did not manage to create decisive breakthrough (that was left to Americans) but they did sometimes succeeded in luring Germans to counter-attack and subsequently lose men and AFVs. Overall, because of their failure to exploit gains, casualty ratio favored Germans in bitter fighting around Caen. For the German part, mostly because of Allied air superiority and improved anti-tank weapons, they could not employ their preferred tactic of concentrating armor and striking hard at Schwerpunkt. When they did attempt that they more often then not suffered heavy casualties.
