DEVIN - An Elders Quorum president is given keys and a High Priest Group Leader is not given keys, but I can see no difference in their duties, responsibilities and stewardships. What exactly are these "keys"? When a temple president is set apart he is given sealing keys. Not just anybody can perform a temple marriage. The sealing key is a specific key. Are there specific keys for the EQ president? What can he do that a High Priest can not? And if there is no difference then why does the EQ president need keys and the HP group leader doesn't?

JOEL - Let's start off with a few quotes.

Joseph Fielding Smith said:
"Every man ordained to any degree of the priesthood has this authority delegated to him. But it is necessary that every act performed under this authority shall be done at the proper time and place, in the proper way, and after the proper order. The power of directing these labors constitutes the keys of the priesthood. In their fulness, the keys are held by only one person at a time, the prophet and President of the Church. He may delegate any portion of this power to another, in which case that person holds the keys of that particular labor." (Joseph F. Smith, Gospel Doctrine, 4th ed. p. 168.)

"The president of a quorum holds the keys, or the right to direct, in that quorum of priesthood. The bishop holds the keys of authority in his ward. The president of a stake holds the keys of authority in his stake. The apostles hold the keys of authority to preach the gospel in all the world and to have it preached by authority." (Doctrines of Salvation, vol. 3 Bruce R. McConkie, Joseph Fielding Smith)

Russell M. Nelson said:
"Each stake president, quorum president, and bishop holds keys of presidency. Their keys control the power of their particular unit of the Church. Those leaders may not only call and release, but they must also train and bear sacred responsibility in order that the mission of the Church be accomplished. Those individuals who receive ordinations or callings have obligations of obedience, loyalty, and understanding." (Power within Us. Russell M. Nelson p. 104)

It's all a matter of obtaining the right to preside. There may not appear to be a difference between an EQ pres. and HP group leader in regards to what they do, but the fact is the only priesthood leaders who receive "keys" are those who directly preside over a specific unit or quorum within the Church. The Elders Quorum President is directly responsible for the elders in his quorum and is therefore given keys to preside. On the other hand, the Stake President is the president over the High Priest quorum(made of several ward groups) and therefore holds the keys to that leadership position.
Your observation is understandable. But even though the High Priest Group leader holds no keys, he has just as much right to receive inspiration for his leadership position in his group as the Elder's quorum President does. And the Stake President does delegate some of his leadership duties to the HP group leader. Actually, the HP group leader is responsible for more programs and more people in the ward than the EQ president(my experience from having held both positions).