Both are good Campgrounds. Shaeffer Heard is closer to the dam off I-85 at the Kia Plant or US 29- Whitetail more mid lake off GA 109.
Once winter sets in they only leave Heard open and usually close Whitetail so you might want to check on any designated closing dates for them. Whitetail is the newer of the 2 but they did some upgrades a year or so ago at Heard. The sites at Whitetail seem a little bit better- but not by much. There are some great ones at Schaeffer Heard. I'd say its a toss up and we love both- some of the most scenic campsitess we have ever camped at in North America.
Both are outside of town. R. Schaeffer Heard is closer to the small burg of West Point, Whitetail closer to LaGrange with more stores etc. Routes in and out of them are quite different.
I live in that general area so if you need any info please feel free to drop me a PM for more specifics.
This route puts you in the area for several touristy visits if that's of interest. Roosevelt's Little White House in Warm Springs. The Callaway Mansion in LaGrange and others.Also note both parks are about 20- 30 or so minutes from Callaway Gardens- definitely worth a visit if you are interested.Traveling south you'll be near enough to stop if you desire at the Army Infantry Museum in Columbus,The Richland Rum Distillery in Richland, Plains, GA (Carters Home), The Andersonville Civil War site, and the pecan, peanut and cotton country of south Georgia.
Have a safe journey! (Weather 60 ish now in this area)