I think having both is probably the best scenario and many people do. I've seen students over the years with extremely high IQ's unable to relate to or even really speak to others, including adults. They were very isolated, often outright rejecting all attempts to include them. My brother-in-law runs the computer department for a major medical school and some years back he had to let go a similar individual because he was unable to collaborate on projects and often said very inappropriate things to coworkers to maintain his distance from others.

Obviously not all people of high IQ are lacking EQ, but can be a problem. Would I give up IQ points for EQ if I was low on EQ? I have a few points to spare I suppose, but I wouldn't give up much. My IQ allows me to understand and appreciate things that are very important to me and give me much pleasure. I wouldn't want to lose those.