How are you crossing from one country to the other -- flight or land? And what are your entry and exit points?
That said, I lived and worked on a kibbutz in Israel for 4-5 months many, many years ago. I did most of my travel in Israel as weekend trips away from the kibbutz. My favorites were Jerusalem (a must-see) and snorkeling in the Red Sea. The Sinai was also cool, but it was Israel then and is Egypt now (giving you an idea how long ago it was that I went). Israel also has some neat Roman ruins.
Of course, if you're into history, Egypt is going to be astounding. I highly recommend splurging for a Nile cruise. You get to pack in all the main temple sites and do it without having to worry about the hassle of transportation, buying your tickets, and so on. I used an Egyptian company to arrange it: Delta Tours Egypt
Delta Egypt : Nile river Cruises : Egypt Budget tour packages : Egypt Desert Safari
They were extremely reasonable in price, especially since I had all the airfare taken care of by myself.
While you're in Cairo, you'll see the pyramids of Giza, of course. Do NOT do them with a tour, though. Simply take a cab or whatever to the site so that you can take your time and explore them at your leisure. Expect the hawkers selling souvenirs and other tours at Giza (and much of elsewhere in Egypt) to be very annoying. Just let their sales pitches slide off your back and keep walking. If they get too insistent, shout "Bess! Bess!" which roughly means "Enough! Enough!" Shocks them when you throw some Arabic their way.
I had a great time in both countries and highly recommend them.