A car battery will last longer if it is used a lot, lead-acid batteries die quickly if they are regularly allowed to drop below 50% charge due to the plates sulphating up (a problem on low mileage cars), heat is the other big killer, and hot under-bonnet temperatures will cause damage in the summer which is not normally apparent until the battery is expected to supply extra power for cold winter starts and generally increased demands on it due to heated screens, headlights, wipers etc.
I used to work for a company that made machinery for producing batteries, and learned to buy batteries by 'weight', which is a good indicator of the number of plates inside them (the 7 and 9 platers - or K-mart specials as they used to be called in USA use the same container size as the 13 platers, but have a lot of empty space inside them).
I don't think your cars computer knows or cares what size battery is fitted, but the biggest ampere-hour size that will physically fit gives you extra starting and reserve power. Take note of the position of '+' and '-' terminals on the proposed replacement battery, because if they are wrong the cables may not reach - and also the terminal size (the GD Jazz has Japanese size 'small' posts).
