Hey John,
I love my Asolo Pumoris. Can't speak for the La Sportivas. Asolos have always fit my feet so well.
I bought my Pumori's last year, and used them on quite a few hikes/climbs around Mt. Baldy, and one hike up to Trail Camp on the Whitney trail with my Grivel G12s. Never had an issue with blisters or break in, even from the very start.
I only use them when I'm anticipating needing crampons, as my G12s don't work too well with my Asolo Fugitives. But when I use them, I really don't notice much of a difference between the two pairs of boots outside of the stiffness of the soles.