Should a product manager be more focused on high-level product features and strategy, or be down in the trenches looking at each and every detail?

Strategy becomes academic (i.e. abstract, useful and irrelevant) without daily/weekly anchoring to what's actually happening.  Trade-offs live in the details, with just-enough functionality for new features being balances against one more bug fix, another drop of incremental rigor in automated regression suites and slightly improved workflow.  Etc. Etc.  IMO, free-floating product strategy quickly inflates into airborne BS.Likewise, long-term product evolution happens one day/sprint at a time.  The journey of a thousand releases starts with this morning's uncomfortable trade-off. Working only the details means that you've ceded decisions to someone else who may be more senior/insightful/better informed.  Or just might be one of those free-floating strategists not tethered to practicalities.

If you are a product manager in your company, you must be able to understand which items need your attention in depth and which ones require you to involved in less intention. High level features are ultimately the most important ones. But keep in mind these will also define the low level decisions. So in my opinion you will have to focus both of them.

Depends on where you are placed. If you are working in a start-up, chances are you would be doing both.  But if you were to be working in a big organization, chances are the tasks would be streamlined and you would exactly know. 

Having said that, it always helps to keep a tab on the general trends in the market place. There are always game changers that always set the pace. In conclusion, you should always view your product objectively and ask the most important question, " Does your product offering evoke Customer Delight? " 

Most of the time it usually tends to be combination of both, depending on what level you are working at, as Lead Prod Man or Sr Prod Manager one would be more focused on High-level features and strategy.

Product Manager should be like a doctor who diagnose the patient by observing different symptoms to figure out the actual reason for his ailing. But we cannot restrict him what points to be observed or what not. It purely depends on the need of the hour or objective he wants to accomplish. 

product manager be focused on developing the product according to the needs of the market as per the feedback of the research development team for the different market segments so that different marketing strategies can be adopted for marketing the product and maximum financial gains can be achieved.

You can't tell in general, the product manager should use all his available resources to drive his product, one of these is what do you need to know about your product to achieve the required efficiency in the projected time frame.

I believe a product manager should get into details, but not deeply as it distract you attention from the strategic  few that you should have

Rather a false choice.  You need to cycle between broad features/strategy and dig-deep details.  Strategy becomes academic (i.e. abstract, useful and irrelevant) without daily/weekly anchoring to what's actually happening.  Trade-offs live in the details, with just-enough functionality for new features being balances against one more bug fix, another drop of incremental rigor in automated regression suites and slightly improved workflow.  Etc. Etc.  IMO, free-floating product strategy quickly inflates into airborne BS.Likewise, long-term product evolution happens one day/sprint at a time.  The journey of a thousand releases starts with this morning's uncomfortable trade-off. Working only the details means that you've ceded decisions to someone else who may be more senior/insightful/better informed.  Or just might be one of those free-floating strategists not tethered to practicalities.In the course of your day, book an hour on your calendar (with no other attendees) for planning and strategy and contemplation and refocusing on what matters.  If you can keep your head out of the weeds for just an hour, the rest of your day will be tactically aligned and your hard work will matter more.