i use capilene boxers, so i can't really advise here. i bought the capilene on the advice of a co-worker who swears by all things capilene. i got them on sale on the Patagonia website, or i might not have purchased them. On sale though they were still expensive cp. to the price you mentioned for Walmart. They function real well, but not owning any cheaper ones, i can't compare.
one suggestion however. if you have the time b/f your trip & the cost is small, as you say, buy one of each from Walmart. Try them out on a day hike or aft/eve hike. See if either performs well enough for you to want to buy more & take them on your trip.
If they fail the test, then you're not out much $$ & you've at least got two pair for yard work, etc on those hot, humid TN days.
Addendum added after B. Tang's post:
I haven't tried the Duofold VariTec briefs, but I have tried D/f Varitec tops. They seem to perform, IMHO, nearly (not quite, but nearly - 80%-90% ???) as well as some Patagonia Capilene tops that i have. So, i think Ben has given you good advice. I bought my Duofold at Campmor (click this link) (often on sale - very inexpensive for reasonably good quality $6-$7 for some of the tops; briefs might be cheaper???). I've done quite a bit of business with Campmor - no problems on any order. They're in New Jersey. I'm in CT. Normal delivery (non-expedited) is 2days once order ships (usually 24-48hrs after placing the order).