I think those two neighborhoods are pretty grim for Chinese, even if all you're looking for is magenta-sparerib and burrito-sized-eggroll American-Chinese fare.
Chinatown is so close, I find it pointless to settle. Some Chinatown places offer delivery via services like Foodler.
Both neighborhoods have respectable if Westernized Thai options, and Back Bay has a couple of places that do not-bad Vietnamese, too.
In the South End, I like Myers & Chang, which is more of a modern pan-Asian place, but never do takeout from it. You could do takeout from Yan's China Star, a little steam-table joint in the back corner of Ming's Supermarket, but I've never tried it.
When I lived in Back Bay, I would occasionally get takeout from Hsin Hsin, your basic brown-sauce American-Chinese joint (it called itself a noodle house, for some reason), but I believe it has changed hands since those days and I haven't been back since that handoff.
Typhoon on Boylston is pan-Asian (Chinese, Thai, Vietnamese, Japanese) and not horrible, but strikes me as pricy for what it is, like many Back Bay restaurants. Haven't been back there in years, either. They're famous in a small way for once getting caught posting a custom-made Zagat plaque that inflated their actual rating, and posting fabricated glowing Boston Globe and Bon Appetit reviews on their website.