While "testing", make sure you're watching shows shot in HD, not SD shows upscaled for broadcast on a HD channel. SD shows on a HD TV are noticeably worse than broadcasts on a SD TV (for the good reason that they've been blown to twice their vertical size).Don't pick news shows or sitcoms either. They're shot in HD, but they're still technically rushed.

Also make sure your set-ups are right for HD. If you watch HD shows in Zoom/Grand Zoom modes ON, no wonder you don't find them as good as they could be.

Another cause is that you're used to watching SD on cable or satellite, on a fairly small TV (24" and less), and now you've switched to HD on a fairly big one. The rules haven't changed: the smaller the TV set, the smaller the pixels, the more the image is perceived as sharp (and in HD, the bigger the TV, the more high quality you need to buy to keep a great picture. LG is average, but on a 37", it should still be very good.

Otherwise, the problem has to be with a poorer than usual perception of the image quality (you're not alone, I work in VFX/postproduction and we see it with clients from time to time. They just can't judge properly image quality, might confuse the SD stuff compressed for editing with the final HD output and so on, even when it's plain as day shich is which to nearly anyone else. And it's not a matter of experience, just poor perception). There's really no mistaking SD and HD resolutions, normally. HD TV has over twice the vertical information (1080 lines instead of 486) and well over twice the horizontal information (1920 instead of 720 pixels) and isn't afflicted by the many problems of the SD NTSC signal, that could make it blurry or distorted or bad at rendering contrasts below and above certain ranges.
So yeah, there's a huge and very noticeable difference, increased even more by the switch to completely lossless digital production/postproduction and film transfer (before consumer HD got widespread, the few last years of SD had been done with digital systems and tapes, but the image was most often than not still compressed, sometimes heavily. With HD, it can still be compressed for broadcast or by cable, but only extremely rarely is it compressed during postproduction anymore.).

HD TV isn't technically "brighter", that's mostly your TV set. There's more definition in the bright areas, however, and in production since HD, we use a lot more the darker and brighter tones and bright saturated colors as they're no longer problematic, the way they used to be in the crappy NTSC signal days.