I believe the differences between the two is mostly to the "no nonsense" approach to the Russians, and the fact that they like re-using designs and equipment that work instead of constantly re-inventing the wheel.
Except... they don't re-use designs and equipment. The current mark of the Soyuz (capsule) has almost nothing in common with the early ones other than a reasonably similar moldline. Soyuz has been modified and updated multiple times, not the least as it evolved from a general purpose Earth orbiter into a very specialized station taxi.
Sure, their spacecraft may look "ugly" (or at least, "uglier") than western or American ones, but they get the job done and they are reliable workhorses.
Reliable... is a very shaky claim given the number of near failures and almost disasters suffered by Soyuz over the years. It hasn't killed anyone in a long time, but it's come uncomfortably close an uncomfortably significant percentage of it's flights. And speaking of flights and workhorses... even though it started flying over a decade earlier, it won't match the number of Shuttle flights until somewhere around the end of this decade at the current flight rate. (Last time I looked, I haven't calculated in a while.) In the same vein, while Shuttle suffered two LOCV accidents, it had zero complete mission failures and only one partial mission failure due to an abort-to-orbit placing it in too low of an orbit. Meanwhile, Soyuz had one pad abort, one failure to orbit, and at least two complete mission failures due to an inability to dock with a space station. (As well as several instances of either the orbital module or the re-entry module failing to separate properly.)
All of which is a roundabout way of saying the comparison isn't really as black-and-white as people would like it to be once you compare the actual Shuttle against the actual Soyuz (as opposed the largely fictional Soyuz the actual Shuttle is commonly compared to) and look at the actual numbers.
 Here's three accounts just covering reentry and landing failures.