I've owned both. The Model 70's I've had were made in the '30s, '50's, late '80s, and in to the late 1990's. I do not currently own a Model 70 and don't really miss any of the ones that I've had.
I've owned four "tang safety" Ruger M77's and one M77MkII. The only bolt action I own currently is the M77RL Ultralight in .250 Savage that I bought new back in 1985. I have absolutely no plans of ever parting with it.
I prefer the push-feed tang-safety M77 over the M77MkII and I'm not as keen on the M77 Hawkeye as I am on the older push-feed, tang-safety models. I prefer the ergonomics of the tang safety being right under my thumb when I mount the gun, as it is on my shotguns and my Ruger No.1. I also vastly prefer the floorplate latch of the the older guns verses the arrangement used on the MkII and Hawkeye that I find so cumbersome to use with gloved hands. All three versions have very light cocking effort. I like the big, easy to feel and see cocking indicators they use. I like the Mauser-inspired bolt stop release. I really like Ruger's proprietary scope mounting system, finding it user-friendly when mounting glass to a rifle and unfailingly reliable in terms of holding zero with all fasteners remaining fastened.
My M77RL in .250 Savage was, until 2009, the most accurate sporter type bolt action rifle I had ever shot and it still groups betwen .660" and .770" with boring regularity. The action on this was slick from new but really has that "glass smooth" feel of classic bolt actions of yore now.
Rugers use investment cast receivers. That's a deal breaker to some people, but in explaining why, it's often obvious that they don't understand the investment casting process or how Ruger goes about doing it. It isn't a deal-breaker to me.
I'm not keen on the cheap "pot metal" trigger guards used on the Rugers, or their light alloy floorplates. I wasn't keen on them back when Ruger had replacements available and I'm even less so in the here and now where they don't. Another nit I have to pick with the M77 is that the stamped steel magazine liner needs fit in the assembled stock and barreled action with a degree of "free float" to it. It it doesn't, it causes accuracy to suffer. Seriously. As ridiculous as it sounds, if the magazine liner isn't right, you can't get the barreled action to sit in the stock properly when the three action screws are torqued to their correct values. Those three action screws with that front one being angled like it is makes getting the barreled action correctly re-mated to the stock a kind of PITA that it isn't with more straightforward assemblies on other rifles. In my experience, the Rugers are HIGHLY SENSITIVE to these screws all being properly torqued if the rifle is going to shoot as good as it can. They can't be to too tight or too loose but all three need to be just right. That, again, is why the magazine liner needs to fit properly. Even if it did when new, it might not now on a wood stocked rifle, as the metal is less inclined to change dimension over time that the wooden stock is. Another thing about the tang safety Rugers is that barrel quality among them is pretty variable but somewhat caliber-dependent as to whether a "tanger" is going to shoot well or somewhat less than satisfactorily. As an example, I'm not the only guy who has a "tanger" M77 in .250 Savage that thinks it is more accurate than it has any right to be, and from the outset, I assumed it shot as well as it did and does because the interior barrel finish is so good. It doesn't take many patches to get it clean and copper buildup has never, ever been a problem. I don't think I've had to use Sweet's 7.62 or a similarly aggressive copper remover on it yet. The .25-'06's also seem to have decent barrels on them, in the main. As much as I dig "tanger" Rugers, I would avoid those in 7 X 57 and .257 Roberts like the plaugue because I seen more than one of them in action but never saw one yet that turned in an M.O.A. performance. I haven't seen many in .308 but those that I have seen all seemed to do 1" to 1.5" with no problem. Ruger outsourced barrels for the "tangers" but started hammer forging their own with the MkII series so they don't have the potential barrel quality issues of the older guns. Those older ones made from '73 and earlier have barrels made by Douglas and they're pretty good.
The only MkII I had was in .270 and while not as accurate as my older "tanger" in .250 Savage, it was a solid sub-M.O.A. grouper right out of the gate with 130 or 150 grain Barnes X bullets over full doses of IMR 4350. It was an excellent rifle. The only Winchester Model 70 hunting rifles I owned that shot as well were push-feed models form the mid 1980's.
I'm not real keen on the Hawkeye. They might LOOK like M77's but they don't feel as smooth to me out of the box as the older ones did. I'd rather have an older one and I'd rather have the push-feed, tang-safety model, obviously, because that's exactly what I DO have.
Rugers get panned for inaccuracy. I've had five of them. None were duds, one was more than okay, and one still dazzles me every time I shoot it. Among my 80s and 90s circle of association, the M77 in .25-'06 was revered by a dozen different people I knew personally. They all had one, and they all were sub-M.O.A. rifles. Most of the .30-'06 and .270 versions I've been around were "hunting grade accurate" and could get down to the 1 to 1.5 inch range with some load development. On the other hand, I've seen some dismal groups from M77's in 7 X 57, .257 Roberts, and .243 -like 2 to 2.5 inches.
But I had a Remington Model 700 Mountain Rifle that was a stinker, too. I don't think Ruger has a patent on churning them out. I do think a Remington is easier to sort out if you get one that sucks than a Ruger is.
Ultimately, it's down to personal preference. I like the Rugers. Someone else might like the Winchesters. I'm not seeing a "wrong answer" either way.