Hey school, I'm lefty too. And I've owned both Rugers and Brownings. And to be honest, both my Ruger 77 and the 2 Brownings needed some gunsmithing to get them to shoot up to their potential. The 77 needed a trigger job and a bedding job. One of the Brownings had to be rebedded and one needed trigger work.
I still have the Brownings but the Ruger went to the gunshop on a trade. (For my second Browning).
Now the newer triggers on the Ruger may solve the trigger issue (the 77s triggers were horribly heavy).
That being said - if your heart is set on either of these 2 models, pick the one that fits you best.

Now if it were my hard earned cash, I would seriously look into the Savage line. I have purchased 5 over the past 2 years and every single one of them can outright shoot. The only complaint I had with them is the el cheapo synthetic stocks which were very flimsy in the forearm tip. But I understand that they have resolved this issue and also came up with a new bedding design that is supposed to increase accuracy even more.
Good luck