When visiting Bratislava with my friends, we've noticed that drivers go very fast, and they often don't stop when a pedestrian is crossing the street (something not imaginable in neighboring Austria).
How dangerous is Bratislava for pedestrians actually, compared to other European cities? Is it only our private feeling of insecurity, or is it generally advised to be more cautious when crossing streets in Bratislava, than for example in Vienna?
I don't share your impression that Bratislava is more dangerous than other European cities. On the contrary I had some nice walks through Bratislava. I also had my share of not-stopping Austrians. But that is only my opinion. If you look at traffic fatalities worldwide, you see that the numbers are comparable among European countries.
source: StatPlanet
Having said that Bratislava is relatively safe, I would remain cautious, even in the safest places. You don't want to be part of the 1.7 deaths per 100.000 people on the Marshall Islands.