Its no general rule that chassidish hashgachas are more on top of the food producers, or known to have more mashgiach temidi’s, in fact some of the private run chassidic hashagchos are not worth too much at all.
But, most chassidish hashgachos have much more chumros and restrictions, and in many cases more of a zero tolerance standard, especially when you’re talking about the big national kashrus org’s, dealing with huge non Jewish companies, that officially have to lower their standards to be able to survive with those “big boys”, versus the frum smaller companies (not necessarily chassidish) have the open option to choose which manufacturer plant to use and with which food processor they would have less kashrus issues, so they can meet a much higher standard.
The chassidic hashgachos are usually also subject to much more scrutiny and challenge by their clientele than the national ones, and the term “chassidish” does not necessarily mean chassidish, it includes a big part of the yeshivish world, its a general term for more strict standards, which it obviously is.