The only two that are extremely effective are oxide and citrate. Oxide has an additional benefit in that it's a larger molecule and goes straight to your colon which reduces the amount that's actually absorbed by the system, pretty much bypassing the stomach, and thereby avoiding possible excess mag if you're also taking another form or forms for other reasons. And most of our systems could benefit from the immediate release of oxygen that mag oxide provides, so there's that ....
Mag citrate is extremely effective as a laxative, but in my experience, much harder to control in terms of dosage effect, often leading to lengthy and unpleasant bouts of diarrhea. It's used extensively in US hospitals as a pre-op complete flush-out, not something you want to deal with in an at-home basis, and is the primary performer in most OTC laxatives for this reason.
And all forms of mag run the danger of arsenic contamination, along with cadmium and lead, so it's important to order from a company you trust, and/or request third party content analysis and certification.
Magnesium can’t be used as a stand-alone molecule, it has to be bound to something else to maintain stability, so the biggest difference in various magnesium products doesn;t come the elemental magnesium itself, but rather from the molecule it’s bound to. The larger the molecule of the substance mag is bound to, the more varied its action in the human system, and the less mag is present by weight.
In my experience, other forms of mag are not as effective, or as predictable and user-controllable in their effects, as mag oxide. For instance, at one point I was taking as much as 2000-2400 mgs of mag glycinate a day, for issues other than constipation, and it did nothing to loosen my bowels. But Mag oxide works effectively, gently, and predictably for me use after use after use, which is why I recommended it ....