These seem to be the two big deaths in the series that people are bothered by (well, and Bodie), and every time I've had this conversation with friends it seems that the people who watched the show as it aired were bothered more by Omar's death and the people who marathoned the show long after it ended are more bothered by Stringer's death. That's not universally given, of course, but it's a trend that I've noticed.
As someone who marathoned, I was definitely more shocked/bummed by Stringer's death just because it was a finished product and I knew I still had two, full, Stringer-free seasons left to watch. As it turns out, of course, the show coped just fine without Stringer Bell, and I still liked those last two seasons. But at the time it happened, Bell had been built up as such a huge character that I couldn't imagine what the remaining episodes would be like without him. In that sense, I think the stakes were higher with Stringer's death.
Omar's death, on the other hand, was shocking more for the particulars of when/how it happened than for the fact that it happened. When you know you're at the last few episodes of a long running series, you expect all the major plot points and character arcs to be sealed off. And when the show is a crime drama, you know that several of those arcs are going to end in death. So in that sense, the fact characters start dropping is less of a surprise in general, but also the "what are they going to do without Omar?" question is less important because it only applied to two episodes. Omar is ultimately gone for a longer stretch of time when he's in New York and in Puerto Rico than when he's dead just because of how the timeline works out.