From my experience with 're-prints' or 're-issues' of games (whatever you would call them), it all depends on the manufacturer as to whether or not the re-issued game title will have a different look from their original release version.
On one hand, you have the 'Platinum Hits' (XBox), 'Greatest Hits' (PS1, PS2) and 'Player's Choice' (GCN) re-issues, which are obviously different from the original release version titles, due to the fact that the cover insert, plastic storage case and game discs themselves are most likely to have a different color to them or simply have some sort of moniker (such as the Player's Choice yellow bar) emblazoned on the top of the cover insert. In other words, it's very easy to distinguish a re-issued game compared to it's original release, thanks to the package and game disc re-decos.
On the other hand, you have companies and manufacturers that re-issue games WITHOUT the obvious 'Player's Choice/Greatest Hits/Platinum Hits' moniker anywhere on the package. The only real indicator of the game being re-issued is usually the fact that 1) the title that was sold out or hasn't been sold for months at a retail chain store (places like EB Games, Target, Wal Mart, Etc.) finally reappears on the shelves and 2), the 'rare/out of print' titles are now being sold for less than what they were previously retailing for. That usually ends up with a price like, say, a game that was originally $49.99 on it's release date is now selling for $29.99 or $19.99.
These re-issued games sometimes do not have any indicators aside from the above mentioned instances in availability and pricing. The game discs and cover inserts themselves are the exact same as the original release version, just without the higher retail price.
Some games that come to mind in terms of being re-issued (usually for the demand they garnered to get re-issued in the first place) are the following:
AirForce Delta Storm (Konami, XBox)
Resident Evil 2 (Capcom, GameCube)
Resident Evil 3 (Capcom, GameCube)
Another interesting thing I discovered was that games like Shin Megami Tensei: Nocturne, Disgaea, Digital Devil Saga, and Rez are supposedly getting re-issues.
Judging that these games are not the 'Platinum Hits' type of games (meaning that they probably didn't sell as many copies as say, Metroid Prime, Soul Calibur II, etc.), I have a feeling that the re-issued copies will look just like the original release versions.
I still remember seeing Xenogears retail for $39.99 at EB Games for the longest time, all the way up until about Spring 2003.
What does everyone else think about game re-issues in general?