Without going into specifics of any particular hashgacha (I agree with LU)
There are differences among Sefardi and Ashkenazi psak halacha when it comes to Kashrus- one well known example is that sefardim do not rely on the leniency that having a Jew light the fire takes away the problem of bishul akum. Other issues apply to Shechita. Because of this, it is more common that an Ashkenazi can rely on a Sefardi Hechsher than vice versa. But, many ashkenazi hechsherim have taken on extra chumros and their shechita too is according to the Beis Yosef (meaning R’Yosef Karo, not the hechsher of the same name), so that Sefardim can rely on them.
That said, there are hechsherim that are considered more reliable and hechsherim that are considered less reliable, so that among both Sefardi and Ashkenazi hechsherim there will be those that everyone “holds by” and those that some people will avoid.