I've seen them both used in the same context, for example, テレビは片隅にあります
In that sentence, would 隅 have the same meaning, or is there some nuance to the two words?
If the TV was wide enough to span across the two corners, it occupies 両隅.
If the room was a quadrilateral, you may put four TV's each on 四隅.
The guests would probably not forget about your awesome TV's, because it remains in their 記憶の片隅 (memory's 片隅). We use 片隅 for this case, as a poetic expression.
片隅 tends to convey a "sad/lonely" message. So if you wanted to place the TV to the corner, 隅 would be fine. But if you wanted to "put that rusty tube in the corner of the warehouse as it won't be used", 片隅 may be the expression you're looking for.
Did you really see テレビは片隅にあります somewhere? It looks odd to me.
片隅 is a nuanced word that typically has a connotation like "a place that does not receive much attention", "a relatively uncrowded part of an area", etc. It's fine to say 部屋の片隅にたまったホコリを掃除する, 教室の片隅で静かに泣いている, 社会の片隅で生きる and such, but it sounds funny if it is used to explain the concrete physical location of something.
To describe the position of a TV, 隅 is the natural choice (テレビは(部屋の)隅にあります). A square room has four 隅. Note that 隅 can have the same connotation as 片隅 depending on the context. 隅っこ is a colloquial equivalent of 隅.