Recent genetic studies make it clear that in the male line Jews are just a subgroup of the Palestinian Arabs. Plotting up a bunch of the world's Y chromosomes shows that all the Semitic Middle Eastern peoples are closely related, with Jews from various diaspora populations scattered about with Palestinian Arabs very nearly in the middle.
The good news is that the genetics of Arabs and Jews have been pretty extensively researched. The classic study dates to 2000, from a team lead by Michael Hammer of University of Arizona. They looked at Y-chromosome haplotypes - this is the genetic material passed from father to son down the generations.
What they revealed was that Arabs and Jews are essentially a single population, and that Palestinians are slap bang in the middle of the different Jewish populations (as shown in this figure).[see the linked article]
The situation in the female line is more complex, with a wide variety of populations represented, typically characteristic of the population where the Jewish subgroup was located. Thus, Jews from two different regions of India carry the the mitochondrial DNA characteristic of those Indian regions. Similar relationships are common with Jewish groups from other countries.
The most likely scenario is that the diaspora consisted mostly of Jewish men, who travelled to foreign countries and recruited local wives. Those who never left Palestine mostly converted to Islam, and represent the original strain, slightly diluted by a modest amount of immigration of Arabs from other nations.
The differences between Israelis and Arabs seem thus to be mainly religious rather than racial - not that that hasn't always been a good enough excuse for people to slaughter each other. Meanwhile, I will probably use this as an excuse to annoy my Jewish friends and relatives by referring to "Jews and other Arabs" on suitably inappropriate occasions - like when they are spouting racist anti-Arab stuff.