Veteran Goaltending: What Good is it?

Sorry to disappoint, but I don't have any statistical analysis to offer.  Just questions.

We have a few days left before the Caps launch their playoff run against the New York Rangers, led by their MVP goalie, Henrik Lundqvist.  Lundqvist undoubtedly has the capability to put forth world-class netminding.  He's a seasoned veteran, is not too old, and is highly, highly skilled.

On the Caps side, we have a sophomore and a rookie in net.  I think Varly and Neuvy are more than good enough to power the Capitals to the Stanley Cup.  Each is highly skilled, can demonstrate great poise under pressure, and has had a very strong season.

The primary difference I see in goaltending between the Caps and the Rangers is experience.  Lundqvist has been in the League, and in the playoffs, for many more seasons than Varly and Neuvy.  I'm getting the sense that this is why analysts are giving the Rangers the edge in goaltending in this matchup, and is a source of great cockiness  confidence for Rangers fans heading into this series.  If I had a dollar for every time I read some idiot saying that the Caps have no established and experienced number 1 goaltender, and that it's a big reason why they're going nowhere in this year's playoffs, I'd be coming on enough money to watch them be proven wrong live and in person.  

Watching our two goalies over this season, I have not seen much in the way of what I'd call 'rookie mistakes' (compare this to Holtby, who could use some tempering/refinement with his puck playing).  They've given up soft goals, but I don't feel that they've been doing so any more than more experienced NHL goaltenders do.  Both Varly and Neuvy have played for 2+ years against high-quality North American skaters, and I think are beyond the point of making 'rookie mistakes.'  Moreover, each has played under very high pressure and done well enough to win.  If Varly or Neuvy make mistakes in net, I think they will be mistakes that they're just as liable to make 5 and 10 years down the road.

If my observations about a lack of rookie mistakes is correct, then I am unsure what marginal benefit years of experience add.  What benefit does experience add to playoff goaltending?  What led people to believe that the Caps would have been better off with a more experienced goaltender this spring?