This is a very subjective question, so there cannot be a single, authoritative answer. However, the two subjects are inextricably connected through their material; a "good reader" wants to read good writing, and a "good writer" hopes his writing will be read by a good reader. The simplest definition of each could be as follows:
- Good Writer: one who reliably creates material worth reading
- Good Reader: one who reliably reads material worth reading
As you can see, even the definitions are subjective. A good writer might be one who creates material that is influential, but many works are influential while being incomprehensible or obtuse. A good reader might be one who seeks out material for mental stimulation or expansion of ideas, but many such works are turgid and boring, or worse, contain no new ideas but are packaged differently.
To my mind, good writing is almost invisible; it flows without focus on the words and sentences, and only after reading does the reader realize how simple or complex the ideas and/or story are. (Please note: we must as a matter of course divide academical or educational writing from storytelling; the two may overlap, but in general reading for pleasure is a different animal than reading for education.)
For some perspective on storytelling, we may turn to Stephen King, an author of great prolificy and popularity (and debatable quality):
...you cannot succeed unless you read a lot and write a lot. It's not just a question of how-to, you see; it's also a question of how much to... You can only learn by doing.
(King, On Writing, Google Books)
King's point here is that you must read to write; only a select few prodigies are able to turn out new material without some background. To write, and to write well, you must read, even if you do not read well; in this case the reading stimulates and births the writing, regardless of its larger value to the literary world.
Vladimir Nabokov, author of Lolita and many other classic works, has this to say on writing:
To the storyteller we turn for entertainment, for mental excitement of the simplest kind... We may go to the teacher not only for moral education but also for direct knowledge, for simple facts... Finally, and above all, a great writer is always a great enchanter, and it is here that we come to the really exciting part...
(Nabokov, "Good Readers and Good Writers," ridge414.com)
Nabokov delineates the storyteller from the teacher in entertainment value, and both from the enchanter in the quality of their writing; many great storytellers are clumsy with their prose or characterization while still telling great tales, and many teachers are flat and tedious to read because they feel their work should be appreciated from an educational perspective instead of an enjoyment perspective.
Finally, teacher Andrew Pudewa has this to say:
...the two most powerful ways to nurture competent writers—are to read to them, out loud, a lot... and to have them memorize great gobs of poetry, thus storing in their brain for life a glorious critical mass of reliably correct and appropriately sophisticated language patterns.
(Pudewa, "One Myth, Two Truths," memoriapress.com)
Pudewa's point is that immersion in the work is what fosters creativity and ability; not that a reader will be by definition a writer, but that the experience of the work will be more influential than even the work itself.
My answer? Writing is reading: you cannot have one without the other, "good" or "bad."