I own LH Ruger 77 Mk II rifles, now customized to other chamberings and configurations, and would not hesitate to own more and keep them original, have owned a couple of LH Ruger Hawkeyes, and while I do not own, or plan to own an American, I have shot them.
I prefer the older Mk IIs, and honestly for the right handed rifles (me being a lefty) liked the older Mk I's as they had the tang safety that is more user friendly to a lefty using a right handed rifle, as compared to the newer versions with the 3 position wing safety. Just my opinion.
I too agree that the older Ruger were better fit and finish to the Hawkeye. (Guess I am getting pickier as I get older!) While some said the LC6 trigger fo the Hawkeye was an improvement over the Mk II, I never noticed, as I had the triggers adjusted to 3 lbs and smoothed up for improved crispness and less creep/over travel. They still shot well, but cannot say that they (Hawkeyes) were any more accurate, or better performers velocity wise, on average than the older rifles.
The Americans I shot performed well, accuracy and velocity-wise. But they are lower price point firearms, and the stocks, fit and finish overall reflected this. The triggers are not as nice. Will they provide adequate service and performance for the average hunter over many years; Yes, I believe so. And one may not be so careful with the synthetic stock and coatings that mitigate corrosion, and therefore they may get banged around and abused more, than a ncer firearm.
Will they be a rifle that many would be want to be able to hand to down through the generations with pride? No, I do not think they would fit this category as well as a Hawkeye, or even better the older Mk I or IIs.
Sorry, I have not shot the Gen 2, so cannot comment on them from a personal perspective. Nor have I handled one. They do look better though. Do they report them to be improved; Yes.
While I may have looked at them more when I was younger and had limited incomes and means to allow affording better quality rifles, I have always preferred finer quality firearms, even if they may have been Rugers, Remingtons and Winchesters, and not Sakos, Sauers, etc. and while I do not mean to to be a rifle snob, I have never been a fan of the Savage and Mossberg bolt action rifles. Just my opinion, but they just did not seem to have those clean classic lines of the Remingtons, Winchesters, and Rugers! Nor did they feel, handle or balance as nice, for me.
Today, I am lucky that I can afford better quality firearms,or custom rifles to get what I want for features and benefits, or better quality wood on the factory rifles I buy. So, again, if I was buying today, I would still be looking for an older LH Model 77 Mk II. But that is just me!