I just stumbled upon this thread, and came across these quotes, that while a little dated are as relevant as ever, so I couldn't resist to add my .02
There is chasam sofer petach tikva and chasam sofer bnei brak. Petach tikva is supposed to be the better hechsher
Kashrus being a very lucrative business, and a huge segment of the population (more so in EY) being Oilem Goilem, I have adopted a few rules of thumb in deciding which Hashgocho to accept "bechezkas Kashrus" (no pun intended):
1. Hashgocho organization/Rabbi MUST be local to either place of production or place of primary marketing (which is when Chasm Sofer BB lost their Chazoko). With exceptions made for production in places where there is no local Kehilla.
2. If it has any of the following words in the title, it has an extra גריעותא: Mehadrin, Mehadrin min HaMehadrin, Chumra, Hechsher. (Note that two of the most widely respected Hashgochos from EY, Eida Chareidis and Rav Landa BB don't say Mehadrin). Also, if the name of the agency has the words BADATZ in it, but the only Beis Din function it performs is Kashrus, it looses credibility in my eyes.
3. If a certain Hashgocho takes over another at a lucrative producer, and all of the sudden many additional lines become "Mehadrin", it raises my defenses.
4. If a certain Hashgocho will claim that they are the best (not specifically stating that they adhere to standard a b or c, which others might or might not, but actually using comparative terms such as better than, etc), relying on the most stringent shittos lechol hadeios, my defenses are up again.
5. When it comes to food establishments (as opposed to commercial producers) I like to know who the owner is, my decision whether to trust or not will be based on a combination of the owner, Hashgocho (and occasionally personal acquaintance with mashgiach on premises whom I can ask questions of).
I don't eat any of the above, I feed it to my garbage if it makes it through my door.
To quote a greatly admired mashpia celebrating his 80th birthday these days: ״מ׳האט אויפגעהערט עסן כשר, און אנגעהויבן עסן הכשרים״