Australia. AIF were all highly motivated volunteers who had to satisfy strict entrance requirements. Australia itself was never really in danger and most soldiers understood this; they volunteered for the adventure, for the chance to test their mettle, and most of all because they had a tremendous reputation to live up to: their forefathers in 1st AIF in WW1, who by 1918 were without a doubt the best troops on the field on either side. They also had probably the hardest and most thorough training of any troops in the war; they trained from the day they joined the army to the day before their first battle, and after every battle they'd be out on exercise excitedly going over what they'd learnt. It was a bit of a sport really, and they were obsessed with being the best.
Take the Australian 6th Division for example, the very first division aus formed (1939) to send overseas. There were conflicting signals from the Government as to whether they'd be going overseas or not, or maybe the militia divs would be overhauled as volunteers and sent instead, so when recruiting opened up many guys, even in the militia, wouldn't join simply because they thought the div wouldnt be sent anywhere exciting. On top of that, recruiters used any excuse they could to deny men entry. This all led to a unit made up of only the keenest, most adventurous type. It also had many highly experienced men (especially officers) who had fought in WW1 (they all lied about that because one of the many ways to be disqualified was to have fought in the last war), and when it was finally ready to go into action (after almost a year of training) it was straight off the bat a crack offensive force to say the least. In fact they soon found the div had enough high quality officer material for 5 divisions, let alone one. on the ever of their first battle, the battle of bardia, the mood was excited but also quite tense; they weren't nervous because they were attacking frontally a fortress with at least twice their men, more guns and more tanks; they were nervous because they had a legacy to live up to, the world was watching them (or at least the country) and they were scared of falling short. These guys actually looked down their noses at other AIF divisions and regarded them as pussies because they didn't sign straight up in '39. reinforcements to the 6th were treated in a similar way
then UK wasted them of course by throwing them into futile campaigns without support like Greece, where many ended up as POWs. lol
ignoring the above, Australians were the best close quarter fighters by a considerable margin; that is beyond dispute