The Tiger could have been manufactured in much greater numbers, but in it would have reduced the number of medium tanks being manufactured. Germeny didn't have as large an industrial capacity as Russia, and so it wouldn't matter which tank Germany had chosen - be it the Tiger, Pz.Kpfw.IV or T-34 - they would still not have been able to manufactured (and field) as many tanks as Russia.
Some 1350 Tigers were accepted in service, and around 1500 were built. On some internet pages I have saved at home it is sugested that Tiger's box like shape was due mainly to help with production, rather then because they didn't learn about sloped armour. Don't know why . They were not really that far appart. It could be because more T34's were built, rather because of quality. Both had same guns, same engines, but T34 was around 25t and the KV around 40t. Perhaps because the germans have attacked Russia when they were just starting T34 production and KV1, and T34 was faster produced then KV1 and in larger quantities. This would be the only reasonable motive as why T34 were prefferd. If we talk quantities, some 40.000 Shermans were built, compared to 32.000 (or 36.000, can't remember now) T34, and some 9000 Pz.Kpfw.IVs. Tigers (or King Tigers) can't possibly be overrated as fighting quality, or tactically. Tigers were not a nightmare of reliability, they costed quite a lot (would be interesting to know if a Tiger killed it's own value in enamy armour), they did consume a lot, and their production was not that complicated. But, everybody knows that or US. Tigers were good tanks, but never in the neaded numbers. Panzerman, I can't see tanks (especially german panzers) as "stand alone killing unit", because their strength came from beeing concentrated in panzer armies, and not spread amongst infantry companies. (Hope this answers Roel as why german panzers were outnumbering russian tanks. Not to mention that most of the Soviet armour consisted of obsolite models)
I understand how Panzer IIIs concentrated in Panzer Divisions would outnumber Russian tanks locally, but that only counts in a tiny timeframe when the Russians hadn't organized their tanks into Tank Regiments and Tank Armies yet. Within this timeframe we see T34s, far superior to Panzer IIIs in terms of firepower and armour protection, fighting more or less alone against concentrated German armour; even so, the few T34s still managed to leave quite an impression on the German armoured forces when they discovered the inadequacy of their weapons against the Russian design. When the Germans invaded the KV1 had been in production for over a year and a half. The T34 was still relatively new, though.
KV 1 started production in september 1939. But there were problems whit it, namely working with 75mm steel is not easy for the russian workers. Not many were built (don't really know numbers, but I guess is under 800), and combined with russian understanding of tank warefare, they were spred with their infantry. (german attack one small front line, and they find a handfull of T34's or KV1's, as opposed to 50 or more panzers) I'd add that germans were surprised to find out the inadequacy of their guns too. Only 88mm guns and 105 field artilery pieces (or higher) made an impresion or destroied russian armour T34 and KV1.
It was a tank designed to suport infantry assaults (more like stugs). So, is not neaded to be small. Besides, in 1941 the germans could shoot at it with 37mm guns, 50mm guns, 75mm short barel guns (which were all useless against it), 88mm guns and artilery pieces. Of all, just the 88 had a real chance to knock it out. High profile came as a price to mount 152mm gun on it. Good to knock around infantry or pilboxes...