Take the low-volume, easy keyword first if your domain is weak, and save the high-volume, competitive one for when you have authority and time to spend. The pivot is your current authority and the timeline you can afford, not the traffic number attached to each term. A high-volume keyword is high-volume because it is valuable, which is why established sites compete hard for it. If your domain cannot match their trust, that term is a long, uncertain campaign, while the easy term is a win you can actually book.
For a weak domain the case for winnable terms is about more than the immediate traffic. An easy keyword is one you can realistically rank for now, and ranking for it does three things at once: it brings in real visitors, it teaches search engines that your pages can perform, and it starts the slow accrual of topical trust. Stack several of these and the traffic compounds while the domain earns standing. That standing is the exact thing the competitive term will later demand, so the easy wins are not a detour from the big keyword, they are the route to deserving it.
The high-volume competitive term becomes the right target once you have authority and can afford the long game. With trust already banked, a contested term is a reasonable next push because you can compete on something better than hope, and you can wait out the months it may take to climb. The instinct to always chase volume skips this entirely, aiming straight at the biggest number while the domain has nothing to back the attempt and the easy wins that would have built its standing go unclaimed.
So judge each keyword by whether you can win it now given your current authority, not by its search volume. If your domain is weak, target the easy, winnable terms first and let them build the trust and traffic you need. Once you have that authority and the patience for a slow payoff, move up to the high-volume competitive terms.