The similarities between Death of a Salesman and Glengarry Glenross are quite evident in the setting (the everyday life of a salesman), the problem of the story (the need to be on top and enjoy a life of economic freedom in search of the American Dream, the atmosphere (hard times, tough competition), and the sad ending in both stories.
First. Glengarry Glenross premiered in London 35 years after Death of a Salesman was first premiered. Mamet was aware of the success of Arthur Miller's Death of a Salesman and basically tried to visualize how Willy's surrounding world would turn into now that the American Dream is officially dead.
In Death of a Salesman, the American insurance salesman is seen as a character who had opportunities and he failed himself. In Glengarry, the salesmen are each other's enemies and they are every man for themselves.
Also, in Death of a Salesman, Willy's only enemy is his own inability to move on and choose the right things while in Glengarry, the character of Williamson has decidedly destroyed Levene, Ricky Roma ruined Lingk's marriage, and Aaronnow and Moss are each other's Nemesis.
Lastly, Ricky Roma is the Anti Willy Loman. Willy still held the traditional and conservative ideal that a good position in life, a good position in the football team, and a good standing with the ladies made you a prosperous provider to your family, and the embodiment of the American Dream. In contrast, Ricky is ruthless and ambitious because he just wants to be somebody- he hardly cares for being a fruitful member of society, but to be a man on top. This shows his avarice, and lack of morality. Even more so than Willy's at his lowest moments.
Both plays seek to reveal a rather disturbing underbelly to the nature of work and, in particular, the life of a salesman. I have always felt that Miller's work has a bit more of a melancholy tinge to it, whereas Wily's condition can be appreciated by more as it possesses more universality. Mamet's work is a bit more on the harsh side, as it shows the level of disloyalty one salesman has towards another in their attempt to stake their claims to financial success. I don't think that this minimizes the work in any way, but rather displays a less humanistic tone that is found in Miller's work. Wily's pursuit of the American Dream is a bit more tragic which can be contrasted to Mamet's work, which is more brutal.
It's obvious that Shelly Levene resembles Willy Loman in Death of a Salesman, not only by age, but how desperate they are when it comes to money and their jobs. It reveals how money is the characters main focus in life and how having money can change the way a man faces reality and their own life. Money can even control a man rather the man controlling the money. Shelly Levene is willing to do anything to get his hands on money/get his name on the board even though it could cost him his job (breaking into the office/lying to his boss-Williamson). When Willy Loman tries to help his famil and his career but fails, his solution is to commit suicide (he doesn't go out of his way to think of better/other solutions--he practically gives up).