What does heaven look like for Protestants and the LDS church? What will be our purpose in heaven and what do both faiths believe will be the reward for their work on Earth?
This is a Partial Answer, because I know absolutely nothing about what the Protestant heaven looks like, but I can explain what the LDS church believes.
Our spirits are children of a father, who lives in heaven, and sent us down here to find out who's worthy to have his glory. We believe that according to our faithfulness in this life, we will find ourselves in one of three kingdoms, or outer darkness (hell).
The Lowest of the three kingdoms of glory (Hell has no glory), is the Telestial Kingdom. A scriptural (D&C, so scripture for us) explanation of this kingdom can be found here. We really don't know what happens to these people throughout all eternity, but they have the Holy Ghost with them, but not Christ or the Father, and can be visited by those in the Celestial Kingdom. Whether they will again go to earth, stay there forever, set up society, etc, we don't know. What we do know is that those in this kingdom have no families, regardless or earthly "marriages". This will be all those who did not accept the gospel, but also did not rebel openly against God, or deny the Holy Ghost after knowing God.
This kingdom is basically for those who accepted and were part of the church but were halfheartedly in it, and were deceived by the world (riches, power, hate, greed, etc) and were thus not valiant in the Gospel of Jesus Christ. A detailed explanation can be found here. Again we do not know what they do, and whether, or when they can progress, but we do know again that they cannot have families, marriage, etc. and that they can be visited by thos from the Celestial Kingdom.
A Detailed explaination can be found here and here, but basically we believe that this is the best, and this is what we are all looking towards. Those who make it here, will recieve the Glory of the Father (our Heavenly Father, or God) and become like him. We will become Gods like him, and we will be able to continue onward with eternal families. We believe that we will eventually be the Gods of our own worlds and have our own spirit children. Although we become Gods, we believe that he will still be our Father, and that we will still respect and worship him as a father.
Ultimately we believe that Family is at the center, and that our eternal Goal is to be fathers, and mothers.
From my (Protestant) point of view:
I wrote about heavens in this blog post.
In short: Heavens are the outer space, in our galaxy and beyond.
But souls of people in heaven also exist in virtual reality (similarly to "The Matrix" movie) to continue their human life for the future resurrection to the physical reality. This is the source of fairy tales about people going around in white robes in the heaven. Soul is a backup for the brain and it continues to exist in a human-like form, to support the future resurrection, continuing this life.
Our purpose in the heaven will be to serve as diplomats to make peace between angels (see my free ebook for biblical foundation of this), that no war would even happen again.
In my opinion, every saved human will receive the same amount of reward in heavens, see this my blog post.