Gonna do some research here just for myself, but figured I'd share the results I find.
Giants drafts since 2009:
'09: Nicks, Clint Sintim (LB), Will Beatty (T), Barden, Beckam, Andre Brown, Rhett Bomar (QB), DeAndre Wright (CB), Stoney Woodson (CB).
A good draft, for the most part. Four of the 7 players drafted have become big parts of the Giants. Two receivers, a OLineman (despite Beatty's struggles) and Andre Brown. Beckam wasn't too terrible either.
'10: JPP, Linval Joseph, Phillip Dillard (LB), Mitch Petrus (G), Adrian Tracy (LB), Matt Dodge (LOL)
After JPP and Joseph - oh my God, terrible. Interestingly enough, Tracy was drafted as a LBer. And I'll say this about Matt Dodge, that dude could kick like a mule but was so ****ing inconsistent. I'm happy Weatherford made it work with the G-men.
'11: Prince, Marvin Austin, Jernigan, James Brewer (T), Greg Jones (LB), Tyler Sash, Jaiquan Williams (LB), Da'Rel Scott (RB)
Outside of Prince and Jernigan....... Williams has yet to develop into much.
'12: Wilson, Randle, Hosley, Adrien Robinson, Brandon Mosley (T), Matt McCants (T), Marcus Kuhn (DT)
Seeing a trend yet?
'13: Pugh (trend breaker), John Hankins, Damontre Moore, Ryan Nassib, Cooper Taylor, Eric Herman, Michael Cox
Outside of Pugh, it's obvious that Reese and the Giants FO do not put a huge emphasis on drafting LBers or O-Line in the top rounds of the draft. I mean, they didn't even pick a linebacker at all in the draft this year! Seemingly, when it comes to drafting OL and LB they shoot for the projects in the later rounds, when it may be time to make a more sure thing in the top round.
I don't think it's too early to analyze some of these drafts. The '12 and '13 drafts can definitely take more time before we start looking back on them and analyzing. Who knows what will happen. I mean, if D. Wilson for some reason never pans out as an NFL running back (knock on wood), that '12 draft is a joke besides Randle.
In my (not so expert) opinion, it's time to switch focus. Go for the OL and LB in high rounds, and go for high risk/high reward types for dynamic positions later in the draft.
I'll maintain that the Giants do have way more holes than OL and LB needs, but drafting at those two positions is a start in the right direction to turn it around.
Draft Clowney, trade JPP for a top linebacker (is that possible? is that even worth it?), run train with a tandem of Clowney, Kiwanuka, and Moore. I love the guys in the middle of the D-line.
This is going off on a tangent now, so I'll just stop.
The point of this post was to show though, that when Giants fans say the FO needs to change their way of thinking, it's in similar terms to these. I think I speak for most, if not all, Giants fans when I say we are quite satisfied with two super bowl wins since 2008
tl;dr - DRAFT MORE LBers and OL IN THE FIRST TWO ROUNDS OF THE DRAFT!