Note that Toby is a trustee of CEA and did most of his government consulting due to GWWC, not the FHI, so it's not clear that FHI wins out in terms of influence over government.
Moreover, if your concern is influence over government, CEA could still beat FHI (even if FHI is doing very high level advocacy) by acting as a multiplier on the FHI's efforts (and similar orgs): $1 donated to CEA could lead to more than $1 of financial or human capital delivered to the FHI or similar. I'm not claiming this is happening, but just pointing out that it's too simple to say FHI wins out just because they're doing some really good advocacy.
Disclaimer: I'm the Executive Director of 80,000 Hours, which is part of CEA.
Re: point 1: The bulk of our policy consultations to date have actually been Nick Bostrom, although Anders Sandberg has done quite a bit, Toby has been regularly consulting with the UK government recently, and I've been doing some lately (mostly wearing my CSER hat, but drawing on my FHI expertise, so I would give FHI credit there ;) ) and others have also done bits and pieces.
In a discussion a couple months ago, Luke said, "I think it's hard to tell whether donations do more good at MIRI, FHI, CEA, or CFAR." So I want to have a thread to discuss that.
My own very rudimentary thoughts: I think the research MIRI does is probably valuable, but I don't think it's likely to lead to MIRI itself building FAI. I'm convinced AGI is much more likely to be built by a government or major corporation, which makes me more inclined to think movement-building activities are likely to be valuable, to increase the odds of the people at that government or corporation being conscious of AI safety issues, which MIRI isn't doing.
It seems like FHI is the obvious organization to donate to for that purpose, but Luke seems to think CEA (the Centre for Effective Altruism) and CFAR could also be good for that, and I'm not entirely clear on why. I sometimes get the impression that some of CFAR's work ends up being covert movement-building for AI-risk issues, but I'm not sure to what extent that's true. I know very little about CEA, and a brief check of their website leaves me a little unclear on why Luke recommends them, aside from the fact that they apparently work closely with FHI.
This has some immediate real-world relevance to me: I'm currently in the middle of a coding bootcamp and not making any money, but today my mom offered to make a donation to a charity of my choice for Christmas. So any input on what to tell her would be greatly appreciated, as would more information on CFAR and CEA, which I'm sorely lacking in.