I say NO.
When I first got my HDTV, I started watching a, yes local-library borrowed AVATAR, then of course I had to look at a BR see what the hubba-hubba is all about, so subscribed to Netflix BR service, and yes AVATAR was my first rental. After seeing the BR version, I go wow, the DVD version looked just as good to me, so I went back again to look at the DVD, back-and-forth. Verdict: BR DEFINITELY has more definition, increased texture/color realism, but if I didn't pay attention, care more about the movie's story, I'd probly, and did enjoyed the DVD version as well. Your mileage and snootyness
will vary, and definitely as mentioned, how it was mastered plays a big role. Google "BR movies to showcase your HDTV."
So I say no fear, enjoy your DVD, but if a BR version comes along, ie.: made by Lucas Films (they care about the AV quality of their movies), by all means look at the BR version see what your are missing.
Note: AVATAR, during the intro scene where the transport plane is about to land, passes some huge bulldozers on the distance, in the BR version the bulldozers really pop even when they are a distance away. In the DVD version, bulldozers no big deal. The scene were Doctor Grace getting out of the chamber, asks for cigarette, the BR version shows the lab with chrome-like textures, in the DVD version, duller. This was on my 46" edge-lit 60HZ LED.