From my own experience of applying, US universities look a lot more at work experience, leadership, and extracurriculars. Harvard wants people who will be stars; there are tons of people out there with good grades, near-prefect GRE, good extracurriculars, and a stellar internship on their resumes; you have to convince Harvard that you will become the star out of all of them. To improve your Ivy chances, I'd study hard for the GRE. If you haven't taken a test like it, it's probably quite strange. In the US, we've been taking tests like it for a long, long time (SAT, ACT, ect), but people still devote a lot of time taking classes and studying for the GRE.
UK universities seem to focus most on academic performance - it seems that being in the top 5-10% of the class (UK first degree) is the most important factor for Oxbridge, although good internships, work experience, and leadership surely can't hurt. Good luck!