I'll try to answer as best as I can.
I don't think Singer's X-men movies are completely bereft of what's core to the comics but there are definitely areas where they are sorely lacking - not as films but as an adaptation. Singer gets a lot of stuff right though. His casting is usually pretty good, he incorporates franchise staples like Cerebro and the school very well, everyone's powers work as they should more or less, he keeps the central conflict on point, and he understands Xavier and Magneto. That last point is probably his greatest strength in terms of adapting the source material.
Where he falls short though are some of the more intimate aspects of the X-men. While all the pieces are there, most of the relationships are a superficial facsimile at best, especially in his first two movies. That's because the first two movies use Logan as the POV character and primary protagonist without ever really establishing his role among the X-men. He's still an outsider in X1 and X2, a loner who plays by his own rules. What Singer fails to establish is a sense of family and belonging the X-men are meant to represent. Logan never really becomes part of that family in either of the first X-men movies. This would be fine if Logan weren't the center point to both those films but unfortunately that's how they're constructed. The result is this constant outside looking in perspective which makes the sense of teamwork and unity that's core to the franchise notably absent. There was nothing inherently wrong with making Logan the central protagonist but he never really makes him an X-man. Logan doesn't live at the mansion, he doesn't train with the X-men, and he fails to develop strong believable bonds with the other characters.
When you look at it that way, it's easy to see why so many of the relationships feel off. Logan continually creeps on Jean but why? He has like three conversations with her in X1 before leaving and about the same in X2 before she dies. And it's not like they develop any of their relationship off screen, we literally see everything that ever happens between them because the movies follow Logan so closely. So where does this deep seeded love for Jean come from? This problem extends to his relationship with Cyclops and Storm as well. He's supposed to be rivals with Cyclops but they should also develop a mutual respect between one another and a bond over their love of Jean. That never happens and instead they never go beyond merely hating each other. Logan and Storm's relationship is even worse considering it's basically nonexistent despite their history of being incredibly close in the comics.
So Logan is the center of these movies and yet his relationships with everyone are shallow at best. Everything about them is told to the viewer instead of shown or developed on screen. And with such a strong emphasis on Logan the outsider, Singer spends most of his energy making sure Logan looks badass instead of developing any kind of group dynamic either on or off the battlefield. So Storm, Cyclops, and Jean all get their moments to show off their powers but never as a coordinated team because that doesn't work when Logan fights alone all the time. Instead what you mostly get from them are these brief snippets of special effects in lieu of compelling action sequences. The vast majority of the standout action in X1 and X2 is centered around Logan fighting by his lonesome.
I want to reiterate here that most of this doesn't make for a bad movie if you're willing to focus solely on Logan like Singer wants you to. But if you care at all about doing the other characters justice, you're sore out of luck. To make matters worse, Singer also liked to throw in popular characters as glorified cameos or just shells of their actual comicbook counterparts. Seeing Colossus in X2 for something like five seconds was such a cocktease. Kitty Pryde is in X1 sorta kinda not really. Lady Deathstrike is a major villain in X2 but shares no similarities with her comicbook character apart from her claws. That just stings because the movies can't even get the core relationships right but still flaunts these other beloved characters in front of you. The major exception is Xavier and Magneto whose relationship is pretty damn good. I thought Singer nailed their dynamic in all his films.
I hope that helped illustrate how these movies feel a little hollow. Again, not necessarily as films but definitely as X-men movies. I should also point out that a lot of these problems were much improved in DoFP - mostly because of the decreased focus on Logan and the use of Xavier and Magneto to drive the story forward.
