I went thru 5 stoves in 3 years (2012 - 2015), but they were all multiples of only two models.
But the first three were purely radiant, and the last two are very convective, so I'll take a stab at the question: A convective stove can affect a change in air temperature in an adjacent room more quickly, as it is heating the air directly, and that air can move to the adjacent room. The radiant stove must radiate their energy to objects in their line of site, which then bring the air temperature up to parity, so their effect will be felt much more slowly in an adjacent room.
However, the opposite is true in the room you're in. You will feel searing radiation if you're in the stove's line of site, much more quickly if you're facing a radiant surface of the stove. The good news here is that even most "convective" stoves have a fully-radiant front window, achieving the best of both worlds.
Also, since you're in italy, where there's a lot of masonry homes... if you have any exposed masonry, just forget a radiant stove. Been there, done that!