Irenaeus was definitely a supporter of pro-martyrdom and according to Moss, believed that the best kinds of Christians were the dead and holy ones (Moss, 116). He even uses the martyrdom of Stephen as a model of orthodoxy in the sense that his courage accentuates the harmony of the views of earnest Christians (Moss, 118). Stephen's death is regarded as a "fulfillment and perfection of doctrine and a copy of the death of Jesus (118). The fact that he forgave his executioners as well as his bold proclamation are evidence of his doctrinal orthodoxy and authenticity (118). Irenaeus believes that martyrs are the true witness for Christ and all others are heretics. He argues that the heretics are those who do not believe that witness bearing is always necessary.
Similarly Eusebius points out that "for some of the heresies have a great many martyrs; but surely we shall not on that account agree with them or confess that they hold the truth. And first, indeed, those called Marcionites, from the heresy of Marcion, say that they have a multitude of martyrs for Christ; yet they do not confess Christ himself in truth" (Eusebius, 5. 21).
In contrast, Clement of Alexandria thought that those who voluntarily or eagerly sought out martyrdom were foolish. However if given the opportunity (but not seeking it out) it was appropriate do choose martyrdom. According to Moss, "Martyrdom for Clement is part of living a life in accordance with the knowledge of God but martyrdom is neither essential to this life nor qualitatively different from that life's other parts" (Moss, 147). In his mind there were other options to prove that you were a good Christian, aside from martyrdom like prayer, being virtuous, abstaining from pleasure, as well as caring for those who were downtrodden. In this sense it seems as if Clement is downplaying martyrdom, something that would most likely offend Irenaeus and Eusebius to no end.
In the Testimony of Truth, there is a quote that backs up Clements idea that seeking out martyrdom is foolish "If the father were to desire a human sacrifice, he would become vainglorious...these are empty martyrs, since they bear witness only to themselves...".