Some info from within the industry that is no secret but most people don't realize.
The thing to remember about broadcasters/streamers/etc. is that 1080p & 720p refers only to pixel count. Many (most) online content providers use algorithms that compress the visual data to save bandwidth requirements but the pixel count remains the same.
The algorithms provide enough compression that the higher resolution can be delivered at a lower bit rate. While still better than SD, this does result in a softer image and increased motion blur for faster scenes.
Technically, they are not speaking false when they say something like , "broadcast in 720p" but that dos not mean that you are receiving the same quality that is present on the original material such as a Blu-ray copy.
Another trick is up-conversion. Just like your DVD or BR player will up-convert SD to HD, it is obvious from looking at it that a lot of HD TV content is merely up converted an SD source. This is not a necessarily bad thing as older shows most often were not filmed in HD so this is the best you can do to accommodate people's big screen TVs.
When it gets a bit more grey is when a provider upconverts an SD movie that could easily have been obtained from a HD source but they prefer to save $ and use thier old source, yet advertise it as being broadcast in 720 or whatever. Technically still an accurate statement, but still an inferior product.
Another thing to remember is that your local TV provider gets it's content from upstream providers. Content is often compressed even before they get thier hands on it. Take, for example only, (I obviously have no knowledge of the true situation for your provider unless you subscribe to our service) The Walking Dead. AMC may not apply any compression to the master source copy it sends to the upstream mass broadcasters. However, these upstream providers almost assuredly apply compression to allow them to send more channels to thier customers, the local cable/TV companies, via their data pipes. In turn, the local cable company may choose to apply additional compression to allow for as many channels as possible via their broadcast media methods.
In short, a lot can happen between you and the zombie. If you want to feel like you are getting the absolute best picture possible, then you really need to invest in the BluRay.
However, a lot of broadcast HD is still Very Good and I'm not knocking the quality of all broadcasters. Also, BR won't help you with new releases if your not willing to wait a few months. I for one, need my zombie apocalypse as it happens or at least with a 24 hour delay so I can watch the PVRed version and skip commercials.
With great power comes Awesome irresponsibility.