I'm assuming that budget includes optic? In that case I would suggest handling the following in addition to the Howa and Savage before you decide: Browning A-bolt, Mossberg Patriot, Thompson Center Venture, Bergarra B 14, Winchester XPR, Tikka T3, Steyr Pro Hunter. The latter two will probably be harder to find locally for that price but can be found without too much effort online.
If that is just the budget for the rifle, then you can probably also add the Browning X-bolt and Ruger Hawkeye.
Either way, try as many as you can and see what fits and feels the best for you. Also, keep in mind that the first corner that is usually cut on a "budget" rifle is the stock, with cheap plastic being the frequent choice. Of the two options you specifically asked about, I have owned both and would probably be a toss up if I were limited to just those two. I like the Savage action and stock options slightly better in that price range but prefer the Howa trigger since I don't really care for the Accu-Trigger.
You can get a Howa barreled action for ~ $500 and put a $200 Boyd's under it. The resulting combo should run circles around a comparable $700 Savage, I'd guess.
I bought a $300 Savage 12FV and upgraded the stock to a GRS ($540 or so). Not cheap, but a solid rifle all around. It's too heavy for a field gun, and the barrel is too long. Also, I now have an $800 rifle with the barreled action from a $300 savage. It's not the model of smoothness (chamber reaming is pretty rough). But it works and hold 1/2 MOA with preferred loads.
I think the Howas are arguably the best value going in terms of quality vs $$. And you can go anything from low budget to top shelf with the stock and be sure you have an excellent barreled action regardless.
ALSO, AND THIS IS HUGE: many places now sell Howa pre-fit barrels with barrel nut conversions that are easily done. So you can gain the main advantage of a Savage without being stuck with a Savage action and accutrigger. (I happen to think my Savage actions are just fine, but I can see why some don't like the accutrigger).
IMO, the Howa trigger is superior to the Accutrigger, and not by a little.