one thing that should be added here is tread pattern. Some tires are designed to be reversible (used both front and rear) others are one direction only, meaning to put them on backwards the rain grooves will not channel water away and could create a more dangerous situation. a lot of it has to do with the tire design and the frame/suspension design.
During and post WWII there was a lot of rationing and shortages, espcially of rubber and metal. Bikes designed during this period (HD, BMW, etc) were designed so that you could potentially use the same tire front and rear in a pinch if you needed to. If they were different sizes you could at least be assured that the front on your bike might be a rear on a smaller bike and vice versa. The shortages in England continued well into the 1950s and you find that tires there like avon speedmasters were designed to work as both fronts and rears. Take a look at all the vintage treds on this page:
http://www.britcycle.com/Products/555/555_series.htmalmost all of them have rain grooves that work in either direction. Your Russian bike is most likely a copy of a WWII era bmw since the russians liberated all the manufacturing dies, toolings, etc during the war and continue to make knockoff BMWs to this day (the chinese do as well) so it is at home running the same tires front and rear.
With the advent of modern tread technology you get uni-directional tread patterns, patternd designed to push water and other slick road substances away from the contact patch. If you reverse this pattern you will find that the channel does not work as well or will actuall trap water at the center of the contact patch. Avon venoms or Metzler lazertechs are a good example of these, their grooves toward the edge of the tire but they only work if the center groove gets there first.
Some tread patterns behave differently when you mix them front and rear. For some reason cb750s need to have a ribbed tire on the front or the heads shake on deceleration, if you run a mismatched tread in the rear this could be made worse (or better - it is hard to say since the manufacturers do not test mix and match with other manufacturers tires). there is a lot of distortion in a tire (it grows the faster you spin it) and tires that distort at different rates or tread blocks that transfer strange forces to the front tread blocks can make the situation worse (or sometimes better).