To add to DaveSSS. The bigger bike will have a longer head tube and so the bars will be higher off the ground and will be higher relative to the saddle height (which remains the same height off the ground because the BB is the same height from the ground regardless of what size the bike is). Sorry, long clumsy sentence!

Head tube length the ONE 'dimension' you can't 'effectively' change, so that's where I'd start... if you want a more relaxed geometry go for the bigger bike and shorten the stem to suit.