At one time, I thought feeling mattered and feeling needed were the same, just different wording. Well, along with the wording feeling mattered and feeling needed are different.

Feeling needed is dependency.
My mom depends on me to help with lifting heavy objects, I, in turn feel needed or am needed.    

Feeling needed can be a good thing. 
Who does not want or need to feel special and depended upon?

Feeling needed can be a bad thing.
Who wants to deal with stress and emotional strangulation when you cannot fulfill the needs of another?

Feeling mattered is to contribute.
Without my typing skills, the paper would not be completed. I, alone with my typing contribution made an impact on the publication.

Feeling mattered is a good thing.
Who does not like feeling like the ‘King of the World’ at times?

Feeling mattered can be a bad thing.
What happens when the feeling mattered feelings do not happen as often as we would like?

Feeling needed gives us purpose and allows us to love others, at times, above ourselves. Feeling mattered does an ego good and allows us self worth and pride.