Some tyres have quite different profile shapes to others, and that can make some bikes unpredictable, hence the comments on trying to fit tyres in pairs or to match ..... that said I have certainly run bikes with tyres from different manufacturers without problems in the past. Ironically I have exactly the same problem myself at present
If you want something a little stickier, try and fit a front from the same manufacturer .... the 016 is bridgestone's "step up" from the 021 isn't it
Alternatively, swap as a pair and sell the good rear on e-bay
Oh, and it's always best to have the stickier tyre on the front
