It is quite normal. For a very good video on this topic, check out James Ehnes and his double disc CD/DVD. In this set he gets to play a number of legendary violins and violas (Stradivari, Guarneri, Guadagnini), and he talks about the differences in bows and the process of picking the right bow for each instrument for each piece. James’ playing is great, but I really enjoy the end of the CD where he plays the same snippet from one song on each of the instruments. Played individually, you might not notice the difference in sound, but played back to back you can hear little tonal differences.