I don't know if I'd say I'm very intense because I've been through some very rough things in life (so I don't know how many of my intense emotions are from that) and supposedly I'm gifted (I don't think I've taken an IQ test).
I've noticed that people who are smarter are more intense in a certain way. I know that often if I tell them something upsetting they're going to really feel empathy similar to way that I feel empathy. On some level I don't understand anyone not feeling empathy that way. I just don't get it/I can't identify with it. Sometimes I think some gifteds are literally dying of empathy. I feel bad for them when they get going.
I notice that there's also this sort of intense curiosity. I remember once I had a secret blog and I could tell when my other gifted friend accessed it because she would click on every single link all over the blog, whereas other people wouldn't have to explore every little aspect. I don't know whether it's simply because maybe her mental processor also goes very fast so where at other people are overloaded with information from looking at one page, she isn't, she has to look at many pages before she gets overloaded processing it ?
I've found some of these things hard, it is very hard when you are very upset about something (I think this is partly from emotionally intensity, but sometimes I think it's added to by constantly taking the long range view of things, "If this happens now, this will happen next year, this will happen in a decade if this trend continues and in twenty years.") If I talk to another person similar to me usually somehow they get what I'm saying, they understand that I'm looking at it as a long range thing. And it seems that they will understand what I'm upset about, and they will understand if I explain to them and not get distracted or having a huge emotional reaction at one thing that I said until I'm finished explaining. Usually I also don't have to go through explaining and "communicating" all the long range implications in huge detail, they just get it. I don't know if seeing the long range view and many implications in detail also engenders a lot of emotional intensity but it often seems to because you instantly sum up all the catastrophes that could happen from now until fifty years later.
On the same note I feel like I sometimes see the interconnectedness of things. I see that one decision or viewpoint people are holding is shooting themselves in the foot with respect to something else they are trying to achieve. It seems that a lot of other people inexplicably can't see this.
I also find that sometimes it seems that holding a few different conflicting feelings/perspectives seems hard for many people. (To be honest it feels like this is hard for me too, but I think often I can be emotionally reacting to one thing while still seeing another thing in the back of my mind).