Veterancy is a bit of a rubbery concept. For units like 12SS and 10SS, the cadres that the units were built around were 1SS Panzer; I'm not sure with 9SS, but both 9SS and 10SS had recently fought their first actions in the East. 12SS was not veteran, per se, although the cadre was. Lehr was similar, due to not all training staff actually having combat experience, with many who did carrying wounds that rendered them more a liability in actual combat. Many of the 'also there' units, primarily infantry, had veterans among them...although these need to be viewed with an open mind, as having burnt out or second rate fitness troops may not amount to 'veteran' status. That said though, experience with doctrine that works, which the germans had, far outweighed the limited training, and incorrect lessons, that the allies had. The US was somewhat better placed than the Brits and Canadians in this regard, but not by much. None of the armoured units in the UK, including US troops, conducted large scale training or exercises...in fact, the Brit and Canadian armour (which did the vast majority of its' training in UK), did not exercise above squadron level in any constructive manner...they were limited to road movement only, outside of the main training areas, and lack of availability for those training areas limited large formation exercises. What that basically meant was that the benefits of the attrition war which Germany was losing, and the lack of fuel/ammo for german training purposes, was wasted...because the Brits/Canadians and to a lesser extent the US, also failed to provide sufficient adequate training to achieve any baseline advantage over the germans. The major lesson that should have been learnt from both the western desert campaigns, and the poor training regime in the UK, was that incorrect training is worse than no training at all...it gives generals an overly inflated view of formation and soldier capabilities. As far as the Brits and Canadians were concerned, a lot of troops died because of the western desert and Montgomery factors (bad lessons learnt and bad generalship).
Bear in mind also that 'training for D Day' was just that...it was training to make one particular day successful. There was no constructive detailed planning on just what was to be done afterwards, nor were troops trained in doctrinal requirements (by this, the 'plan' consisted of lines on maps of where the troops were supposed to be by certain dates, and timelines of when towns/etc were supposed to be held by the allies, but no outline concept or detailed plans for actually getting there).
In game terms though, think of it as thematic....germans experienced, allies not.
