As someone who found The Israel Lobby thesis to be profoundly misguided, it really shouldn't be any surprise that I find its new counterpart, The Arab Lobby, to be pretty silly as well. Hussein Ibish reviews the latter here, though I wish he had provided more specific examples about where he thinks the authors go off the rails, the broad points are sound.
In general, the problem with these sorts of arguments is twofold. First, they nearly always have an insanely reductionist account of "American Interests", creating an implicit baseline of what the U.S. "would" be doing were it not for the "lobby", and then measuring the lobby's influence based on how far it can get us to deviate from our basic interests. But that's not the way interests work--we don't just have interests in the abstract; we're interested in various principles, resources, and situations, all of which are open to political and democratic contestation, and lobbies usually try and convince policymakers to adopt one constellation of interests over another. So yes, if the U.S. really didn't care about democracy (adopting a pure W&M-style neo-realist framework that only cared about defensive security) our position regarding Israel would probably change; if the U.S. really did care about democracy our position regarding Egypt would change. We blend lots of interests together, in a variety of cocktails. And that's okay.
Second, they usually collapse many different perspectives under a single heading. Ibish claims that The Arab Lobby does this by creating blanket groupings of organizations as either "pro-Israel" or "pro-Arab", we know Mearsheimer did this with his wretched list of good and bad Jews. I agree in principle that we can characterize groups ranging from J Street to ZOA as "pro-Israel" in some sense or another, but it seems very bizarre to characterize them as being part of a cohesive "Lobby".
And this, in turn, gets at the fundamental problem with these comparisons between the power of the "Israel Lobby" and the "Arab Lobby"? When you define the Israel Lobby as broadly as do Walt and Mearsheimer, encompassing everyone from the ZOA to J Street, the only thing they have in common is that they don't want Israel to die. Is the sentiment amongst US policymakers that Israel shouldn't be destroyed stronger than their sentiment that, say Saudi Arabia shouldn't be destroyed? I guess, but (unlike with Israel) the potential destruction of Saudi Arabia isn't really on the geopolitical table. In terms of more specific policy initiatives where "the Israel Lobby" is internally divided, it becomes more difficult to sustain claims of unique power. Israel gets lots of American weaponry and aid; so does Egypt and Saudi Arabia. America has security guarantees with Israel, but it likewise has them for Arab neighbors.
Given the unstable nature of concepts like "interests", the widespread disagreement over what it would mean to "support" Israel or Arab "interests", the differing geopolitical contexts which mediate what each group has to request and how much pushback their is against their demands, the question of whose Lobby is bigger is effectively meaningless. These questions are nearly always used as a smokescreen (author protests notwithstanding) to act like somebody is subverting the true needs of the American nation, and I find it aggravating.