I guess it all comes down on how you define prestige. And for this question it also depends on the timescale you put on it. In my opinion it is something like this:
1 year: 2nd Tour > 1st Giro
5 years: 2nd Tour = 1st Giro
10 years: 2nd Tour < 1st Giro
I'm basing this on the general public, since it is the general public that defines prestige, not the hardcore fans. A second place will get you lots of media attention, lots of sponsor interest and a nice salary raise. Far more so than winning the Giro would, unless you are Italian. The general public will have a far better idea who got second in the Tour than who won the Giro. Prestige in my opinion means attention given. The attention to anything in the Tour is far bigger than anything that happens in any other race. What a cycling team eats the day before a stage is more important than who won a stage at the Giro. Of course that is talking from a general public point of view and not my personal opinion.
However as time goes by, palmarès gets more important. Your second place in the Tour will be forgotten faster than your win in the Giro. The more times goes by, the more important your win becomes.