Unless you live and breathe Stargate SG1 there is no benefit to buying this DVD, at all. There are a few changes but they do not alter the film enough for the casual watcher to notice or even care - in fact the new version does not introduce the series.
The biggest changes are in the O'Neill meets Hammond encounter and the Carter introduction, which moves along much better. The harem and nudity scenes are gone and a couple of scenes have been extended (and it is just a couple) and some have been reedited using the original 16:9 format so they appear wider (there is a nice two shot of Jack and Sam drinking the moonshine) and some unused footage has been introduced. The ending is different as well, meaning that this version is a standalone film and not an introduction to the series, as a result seven minutes of "unnecessary" footage has been removed. As the whole of the Kawalsky takeover is missing the next episodes in the series do not follow on, so I really fail to see the point of this "movie".
The music has completely been redone, and is better, as has the whole of Teal'c's dialogue. Other dialogue has been removed and a couple of lines have been added, but unless you watch the two versions side-by-side the changes are so small as not to be noticed.
There are, however, noticeable new CGI elements that add continuity to the series (the wormhole puddle and tunnel for example). The new gilder scene is nice, as is the "snake" coming out of Teal'c, but they are not worth buying a whole new DVD for.
If you are new to Stargate SG1 then it would be a good introduction, but if you own the original Children of the Gods don't bother with this new version; there is just not enough to make it worth it - a few new CGI effects and reedits do not make this anything more than a rip off.