I’m trying to recall what the gradings are, but my question is:
what does it mean when grocery stores boast USDA Top Choice or Prime Choice, etc. (IIRC)? Also, does this relate to the fat content at all, or how tough it may be to chew?
Related to this, does it really matter if it is Angus beef? And, is the best beef from corn-fed (as opposed to grain fed) cattle?
That’s my beef on beef! 
Here’s the USDA’s take on it. They have another page that is kind of hokey (I think it’s geared towards kids) but has good info. (Gradings are Select, Choice, and Prime. You will generally not find Prime at the grocery store, the restaurants generally get first dibs on it.)
Angus is basically a brand name with their own standards that go beyond USDA.
USDA grades have nothing to do with quality. The beef grades are intended to predict the palatability of the meat by observing the amount of fat “marbled” through the meat, as well as its maturity (judged from color of the meat and developmental characteristics of the carcass). The health of the source animal is a minimal pass/fail test, and the nutritional characteristics are not a consideration.
This PDF file gives the actual methods for evaluating beef, along with a handy table that describes the specs: http://www.ams.usda.gov/lsg/stand/standards/beef-car.pdf
The three grades that are generally sold to US consumers are, in descending order of quality, Prime, Choice, and Select. In reality, it’s almost impossible for a consumer to get hold of Prime cuts; almost all of it goes to restaurants. Ocassionally, a really good butcher shop will have it, but that’s rare (unintentional pun, but welcome, as always).
The USDA has five other classifications, some of which are not (supposed to be) sold to consumers. IIRC, they are, again in descending order of quality, Cat food, Dog food, TV Dinner, Fast food, and Hospital/Airline food. 
Just kidding. They’re actually Standard, Commercial, Utility, Cutter, and Canner. Standard is often sold as “store brand”.
Angus is a breed, like Gurnsey or Longhorn. Given two equal quality samples, one Angus, one some other breed, you may be able to detect a difference. But, whether it’s better is a matter of opinion. Of the two best steaks I’ve ever had in my life, one was Angus; the other wasn’t listed as such. Cornfeeding can also impart a slight taste difference, but it’s pretty subtle, and easily overwhelmed by sauces, seasonings, or “grilled taste”.
One breed you can supposedly taste a huge difference is is Japanese Kobe cattle. Some beef afficionados say that Kobe beef, due to a higher fat content, taste like American steaks tasted a few decades ago before we started breeding leaner cattle. Some reviews I’ve read rave, some say the fat content is so high the beef is too mushy. Haven’t had it myself, it’s really expensive and I’m not allowed in those sorts of restaurants.
In the U.S., most cattle are fed a mix of corn and other grains (like wheat or sorghum). I think what you’re really asking about is grass-fed beef.
In my opinion, grain-fed beef is more tender and flavorful than grass-fed. During the 1970s there was a blight that severely reduced the U.S. corn crop. Livestock feed prices went through the roof, and some cattle producers tried feeding grass or hay to their herds. This resulted in the common complaint “you can’t get a good steak anymore.”
Of course, that in no way speaks to the nutritional value or healthfullness of the beef.