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Done both.
Gavia is a very beautiful climb, where you end up above the snow level, riding along a road cut into the snow, through an old glacier at the top, its awesome and quite challenging.
Mortirolo is for masochists. It's insane how truly ridiculous the unrelenting gradients are. There are no views to speak of, its all very steep switchbacks in tree line on a narrow slippy road, leading to a concrete path at the top. If you're carrying luggage you'd better have very, very, low gearing. It's not as enjoyable or rewarding but I guess everyone has to do it once to make every climb look easy in comparison.
Doing some route planning for a week long circuit from Innsbruck in August taking in the Stelvio, and some of the Maratona climbs. When getting from Bormio towards the Dolomites we have the option of Passo Gavia or Mortirolo. The latter is more famous but steeper (assuming the classic ascent from Mazzo di Valtellina) and has fewer views. The Gavia is higher and the approach from the north-west is supposed to be pretty if not the classic Andy Hampsten Giro climb.
Has anyone done both? and have any recommendations? We'll be credit-card touring with a Carradice on road bikes so both are probably do-able.
Cheers
Simon