The Jazz has been the leader of this segment for a very long time. It is a very, very good car. Does almost everything well. The Swift is the new challenger to the throne, well in Malaysia at least, and it is doing pretty well for it self.
Looks? Subjective, I liked the Jazz a lot last time. Not now though. Might be because of the sheer number of them on the roads. Swift has very funky looks. Very European as well, which is good.
Performance? The Jazz VTEC has 110 bhp but the iDSI only 88. The Suzuki has 100 bhp.
Handling? I've heard very good things about the Swift in this department. Not one of the Jazz's strong points, not a weak point either, just nothing special.
Build Quality? Will have to go with Honda, but that said, the Swift is also superbly put together and has an air of quality about it.