If they're both marked 700, they should fit (I think Vittoria makes that tire in a 650, too, and if you got those by mistake, they won't work). Width (the second number, as in 700x23) isn't a major factor in tire fit.
For what it's worth, though, I've had a hard time mounting Vittorias on a couple of my wheelsets. They just seem to be tight. In one case, I broke four plastic levers, finally pried them on with a screwdriver, and then when I had a flat a few days later, couldn't get them off on the road (I've been riding almost 40 years and if there's one thing I've learned, it's how to fix flats). I called for a ride home, then cut the tires off and threw them away, just so I wouldn't have to deal with them.