I cant imagine either the Irish or American passport will make much difference. I was there for Xmas past with a group and what I do know is that the security is horrendous - they may go through every item of your luggage, my purse and ATM cards were taken out and scanned. I was questioned in great detail on why I had Morrocan, Turkish, Egyptian, Jordian and Malaysian stamps on my passport, and you really are treated like a potential terrorist. The two people out of our group who had the most hassle were a New Zealander, with Indian family and an English guy of Goan (Indian) family, they were taken aside and questioned in detail about their reasons for visiting Israel while the rest of us (white Caucasian), stood and waited for them. I'ts a good idea to take a good book and just be patient in the knowledge that it could be a slow process.