A 313 Roadster will be about 150 kilos heavier than a 276 Coupe, so the extra weight will give the coupe the edge on performance. Having access to both a 276 coupe and a 313 roadster, I find the main noticeable difference is that the pull in top gear from say around 50 is considerably better in the coupe, drop it down a gear or two though and there's not much difference. The roadster does make a nicer noise though . Also the 313's headlights are good, the 276's are just about adequate.
Leaky roofs are common in the roadster, ours has leaked slightly on both sides at one stage, for us it's just been a matter of pressing the seals around the top of the window back into place every few months as they seem to work loose after a while.
Other driving differences, well you have to be pretty careful while reversing in a roadster, I backed into a low wall (luckily at about 1 mph) that I didn't even know was there .
Pete