Well, I know that BCPs in general always have a warning that they can cause strokes (it’s a very rare side effect, but it’s possible), and that this is also something that really only applies if your family has a history of strokes. They even tested me for whatever it is that would put you at higher risk since I have two (half) sisters who have had strokes, and they were able to say that I didn’t have the same underlying condition that caused theirs so I wasn’t at risk. Anyway, since blood clots can cause strokes (I think), this may actually be the same thing that you’re talking about, and if that’s the case, I don’t think there’s any BCP out there that doesn’t come with that warning. Your doctor can probably talk to you about the risk of the blood clots or if there’s another BCP that you’d be more comfortable taking, but I can say, at least about the stroke thing, is that it really is a very rare side effect, so you’re very unlikely to have to deal with that. Also, remember, smoking increases that risk majorly, so that means that even as rare as it is, a lot of people who have it are the ones who are smoking while taking them. If you take care of yourself and don’t have any major risk factors already, you should be just fine. But, like I said, ask your doctor, since I’m not a medical person in the slightest and I really don’t know.
Oh, and I can’t remember which ones I’ve been on–it’s been a long time. I never really had side effects from them so I couldn’t talk much about the differences between them. Best of luck!