The policies vary between airline.
In most cases where multiple levels of lounge exist, business class would be considered "higher" than status-based access. For example, United Airlines "Polaris" lounges are only accessible by Business Class passengers, whilst those with status travelling in Economy are relegated to their lower-level United Class lounges. In many cases these business class-only lounges are significantly better than the status-based alternatives.
The same is also true at the Turkish Lounges in the new Istanbul airport as you mentioned. In the old Istanbul airport this was not the case and there was a single lounge used by all eligible passengers, however even then there were specific perks of the lounge that were only accessible for business class passengers - such as the use of the sleeping rooms, or the direct land-side access to the lounge (which included it's own security and immigration check-points).
Lufthansa Group airlines (which includes Lufthansa, Swiss and Austrian) for some reason have this reversed - Business Class passengers have access to their Business Class lounges, whilst those with status (in any class) have access to their Senator Lounges. The "Senator" lounges are deemed to be better than the normal lounges, but in practice are generally pretty much the same as the business lounges - with potentially one or two additional minor perks such as slightly better food or alcohol.
Lufthansa also operate "First Class" lounges in some location which are a higher level of service than both their Business and Senator Lounges, and only accessible by first class passengers. To some extent, these lounges are the nearer equivalent of the lounges like the United Polaris lounge - especially given that most airlines now days no longer offer First Class.