Overall, tank losses for the germans in normandy were heavier than those suffered by 21st AG. But this was from all causes . As of 31 July the OQu at OKH reported losses in france to the end of July as:
Pz II – 2
Pz IV (k) – 1
Pz IV (l) – 273
Panther – 197
Tiger I – 30
BefPz III – 2
BefPz V – 8
BefPz VI – 3
BeoPz III – 2
StuG III/IV – 95
Unfortunately August losses appear to be badly underreported while September is highly over-reported (largely, i think, because of the political machinations occurring in Germany at the time) , so it is difficult to ascertain just when all losses occurred.
On the allied side, Losses were reported June-December 1944 on a monthly basis by the MG RAC, 21st Army Group.
June – Sherman 66, Cromwell 42, Churchill 16
July – Sherman 186, Cromwell 28, Churchill 17
August – Sherman 547, Cromwell 143, Churchill 142, Challenger 2
Note that there was a lot of "catching up" that was done in August. It is obvious that the June losses are underreported for one thing. That was a consequence of the system, since those vehicles KO'ed or not fit within 24 hours were, in theory at least, to be evacuated from the division to an army repair depot where they were often held for some time before being officially "written off". Also note that according to the administrative orders issued, tanks in the last category were only supposed to be reported as such once, then they would be dropped from the unit report. However, that seems a rule more observed in the breach than anything.
First US Army tank status reports were made irregularly during June; daily reporting only became normalized in July. Thereafter, with a few exceptions when days are missing or units did not report, daily reports were made for First Army. Then after 12th Army Group became operational, reports were made for all units assigned to the First, Third, Ninth, and Fifteenth Army. Losses were initially reported as a cumulative total for the first 26 days after D-Day (6 June-1 July) and thereafter on a "weekly" basis (that actually varied from four to nine days).
Strength, 22:00 29 July
M4 (75mm) 748
M4 (76mm) 95
M4 (105mm) 48
M5 541
Losses to 1 July
M4 (75mm) 187
M5 44
Losses 2-29 July
M4 (75mm) 208
M4 (76mm) 12
M4 (105mm) 4
M5 67
Why would the germans suffer heavier losses than the allies, despite the superiuority of their tank park. There a number of factors at work..numbers, airpower, losing ground artillery, all played their parts, but at the very heart of the german defeat was their attrocious (relative to the allies logistic support) supply chain in operation at that time. This arose because of the interdiction campaign, mostly, and a major reason why they lost the campaign in the finish.