This is a very, very, silly assumption. Writing LORs is part of every professor's job, how do you think undergraduates get into top programs? They get letters from top scholars. How do they get them? They take their classes, they do independent studies with them, they get them to advise their senior theses, and they work as RAs for them. Of course good undergraduate students get good letters from top scholars at top programs.
As for where you should go, I'm less bullish on this than other people here. It's more about what you do while you're there than which one you go to; they both have fantastic political science programs, with good faculty, and with plenty of undergraduates that end up getting into top PhD programs from both. If it were me? I'd go to Berkeley because it's a better school in the general sense, but I don't think I'd make this decision based strictly on a criteria of political science programs.