You yourself acknowledged the different circumstances, so I hesitated to post but there are certainly some important considerations there:
1) The martyrdoms among the first and second generations of Christians were a direct witness to the Truth of their witness. That is, the fact that 11 of the 12 apostles and so many of the 70 and beyond were willing to die for what *they had seen* was a witness that they actually believed they had seen it, it was not something they were making up. That particular practical force obviously can't apply later--martyrdoms now prove that the modern martyrs really believe that St. Peter and St. Paul and the rest saw what they said they saw, but it doesn't have the same evidentiary value as St. Peter and St. Paul's own martyrdom.
2) The Roman persecutions were intermittent. When they occurred, the Church suffered, people died and fell away. And then as soon as the persecution let up, the membership exploded. The membership didn't explode *during* the persecution. You can see the same effect in Russia, once the Soviet regime and its persecutions ended, the Russian Church's membership exploded. In Islamic lands, the pressure has tended to be much more consistent (though it might be an interesting exercise to map the variations that do exist with the growth or lack thereof for the local churches--to the extent it could be established).
3) Christianity in Rome was moving into an essentially open marketplace--even if Christianity itself wasn't free, there was not a single overarching competitor. IOW, there might be a great deal of social pressure on individuals not to become Christians, but there was not nearly as much for them to *stay* devotees of Mithras, or Cybele, or Isis, or neo-Platonists, etc. Whereas in Islamic countries, the social pressure is both directions--don't convert to Christianity, but also don't leave Islam. Factoring in there somewhere may also be the fact that Islamic persecution is specifically focussed on conversions. The level of persecution/oppression of existing Christians varies across time and geography, but the on-the-books legal directive for converts is always capital punishment. Thus, Rome's blanket persecutions grabbed many people who had been Christians for decades and gave them the choice of renouncing or being exemplars; Islam on the other hand focuses most strongly on the person who's been Christian for weeks.
just some thoughts off the top of my head.