Imagine a scale where a song’s melody is located at one extreme and its chords are on the other.

If a song is highly dependent on the chords — so much that the chords almost define the melody, then the melody suffers. The verses to “Hotel California” are a good example of this. (It’s still a great song for other reasons, just not for the verse melody.)
If, on the other hand, a song has a really strong melody, and the chord progression is relatively standard, nobody will notice. No normal listener pays attention to the chord progression if the melody is strong enough.
How can you determine what a strong melody is?
One way is to sing the song acapella with nonsense syllables. Can you tell where you are in the song and what chords are implied when la-la-la-ing the melody all by itself?
Another way is to visualize the melody, either on paper or in your head. Look at the shape of the melody like a sculpture. Does it have interesting dips and curves? Does it jump around? Does it soar? Sink? Is it distinctive — not just melodically, but rhythmically? Is repetition used creatively? Are there interesting variations? What sort of melodic range is there?
Despite these suggestions, there’s still no absolute rules for strong melodies. Not even a smart computer program could analyze a song’s melody and 100% accurately determine whether it’s “strong.” That’s because “strong” depends on musical context and your personal taste.
Burt Bacharach may write a great melody with a huge melodic range, surprising rhythmic turns, and artstically interesting melodic jumps. This can be a valid definition of a great melody.
But it’s a trap to think that great melodies can only fit this mold. K7′s “Come Baby Come” has probably about four notes in the melody for the entire song, yet it’s a strong melody that works. And it goes against all of the qualities that a Bacharach melody might have.
And it doesn’t matter what I think are the ingredients for a great melody, it matters what you think, because you’re the one writing the song. Analyze the melodies you love. Use the above suggestions as a starting point for figuring out what makes those melodies tick. Then make your own rules for what constitutes a strong melody.