They are two different vehicles, with the Jazz being a subcompact hatch - geared more towards a sportier ride and the Matrix as a microvan - more spacious, comfortable and has a stronger engine.
Fuel Consumption - My Matrix CRDI's fuel consumption is comparable to the Jazz 1.3l, but the Matrix has a more powerful low-end torque rated at 174lbs/ft.
Space - Matrix's interior space is quite comparable to CUV's.
Ride/Handling - Matrix absorbs bumps and potholes better but because of its height relative to its length and higher driving position, it has more body roll compared to the sportier Jazz. It depends on your priorities - comfort or performance?
When I chose the Matrix over the others, I was looking for a short, spacious and powerful "econobox." Something good for hauling, with a higher seating position and decent legroom/headroom.
If you're into subcompacts, why not take a look at the Accent CRDI and even the cheaper Getz CRDI as well? They'll feel speedier because they weigh 200+ kilos/440+ pounds lighter than the Matrix. They all come in manuals though.