In my experience, you are more likely to find the 'big stuff' down south. There are companies there (Marsa Alam) who run livaboards, Emporer spring to mind. Elphinstone will more than likely provide u with oceanic white tips. For me, the most rewarding is doing a livaboard as you can get out to the Brothers, St. Johns and various other places. Some of these dives, though, are not for your beginners due to sometimes strong currents.
However, if you go to Sharm at the right time of year and get a boat up to the Straits of Tiran, you may see Tiger shark. Hope this helps
Doc