I wish I still had the two comparison pics to show you... A guy with an "amateur" DX camera, D200 class with a $1000ish telephoto lense, took a pic of an F-15 taking off at an airshow. The plane was banked up so you could see inside the cockpit. It was a beautiful shot, and you could even see the pilot sitting in the cockpit including where his legs were.
The comparison shot was from a professional photographer with better glass and a full size sensor. Maybe $12,000 worth of kit. You could see every panel line, and you could clearly see the pilot's lineup card on his leg and even see some of the writing and lines drawn on the card. The first photo was very nice, but the second one was jaw dropping.
It depends on what you're doing. Do you want nice photos suitable for framing and enlarging, or do you want holy crap that's awesome professional photos that you can crop and blow up and maintain amazing levels of detail and sharpness with fewer digital artifacts that either look weird or require time and photoshop skills to edit out?
The full size sensor cameras are coming down in price, but then you're tied to FX glass. FX lenses are more expensive but often higher quality. Again, it depends on what you're going for. For me personally, the balance tipped towards getting a "nice" DX Nikon and then saving up for really nice glass to go with it. FX glass on a DX camera will often result in greatly reduced edge effects (less pincushion or barrel), so you can use popular FX lenses on a DX camera with good results.
Putting it in perspective... My last Nikon cost $800 for the body and the kit lense, and the lense I want to get for it costs $3500. And that lense is considered at or below entry level for pro use. If you're serious, then go big or go home IMHO. If its just a hobby, then get a nice body and spend some real money on glass. A good lense will likely last far longer than the body too, and they're easier to resell or trade in.
