Additional information:
I think both the previously mentioned Glantz and Newton notes that Russian "Soviet archives" opened up for the researches recently (about 2000, maybe in 1995, 50 years after WWII finished) with vast amount of information, so I credit to this fact that works after 2000 give relatively precise numbers.
Also Glantz says that Western researchers had only access to the memoirs of German generals, and Wehrmacht archives.
Also Glantz says that during the war the Germans had awful military intelligence about Soviet troop movements and they only saw amassing troops and constant Soviet offensive preparations everywhere. (When the 2nd Hungarian army was destroyed at Voronezh the German higher command did not believed our reports that the Soviet attacked, and they sent an armored group to counterattack when the battle already lost.)
Karsai writes that the German reports after the battle launched did not talk about a breakthrough attempt, but a preemptive strike, and the elimination of amassed Soviet offensive forces. (This point can help understand Szálasi better.)
Commager states that the Germans and the Soviet launched attacks simultaneously. Then he says first the Germans attacked with large amount of armor.