Standard ("Ballard") specs* for .44 caliber barrels only call for grooves that are nominally 0.0025" to 0.003" deep. MicroGroove specs* call for grooves that are nominally 0.0015-0.002" deep.
It is very difficult, with the naked eye, to tell the difference between 'Ballard' rifling and 'MicroGroove' rifling. ....Because there isn't much.
*(I refer not so much to SAAMI specifications, but what
actually gets produced by firearms and barrel manufacturers.)
The problems presented by Marlin's MicroGroove rifling aren't really related to groove depth being "too shallow", either. It's the fact that bore diameter is often within 0.001" of standard bullet diameter, or OVER bullet diameter.
Regardless... Henry does not use MicroGroove barrels. For that matter, neither does Marlin (and hasn't, with any center-fire cartridges, since 1998).
Typical bore and groove diameters, just for reference:
MicroGroove: 0.428" bore / 0.430" groove (or, with Marlin model 444s, 0.429-0.430" bore / 0.4315-0.432" groove).
Ballard: 0.424-0.426" bore / 0.429-0.430" groove.
Cheaper barrels (such as on H&R 1871, Rossi, and Taurus rifles) can be anywhere within either range. I know of at least two .444 Marlin H&R Handi-Rifles that are "Ballard" rifled but slug at 0.430" bore / 0.432" groove. So nearly nothing commercially manufactured will engage the rifling in any useful way. Bullets from those barrels show substantial and clear evidence of "skidding" across the rifling.
So, what I ended up doing there, with my unplanned babbling, was point out that you should forget about 'MicroGroove vs Ballard' and just buy quality. Henry qualifies.