The Sheraton is in my opinion nicer than the Rennaissance. Yes, the Dan, Hilton and Sheraton are quite expensive. But El Al have deals. And Dan Hotels also offer deals. They have a web site. The Sheraton in TLV have a nice pool. I stayed at the Sheraton in Jerusalem. It is very well located and quite pleasant.

I am sure that security on BA flights to TLV are just as strict as El Al. I have never found it to be an inconvenience.