Let me contrast the Remington in 7.62x39 and the handi-rifle in .357 mag.
The finish of the Remington, with checkering, is more elegant.
The fit of the wood of the Remington is better, but perhaps not on the high-end handi's.
Remington's are made in Russia.
Of all the Handi's the .357 has an incredibly looooong throat, as does the Rem in 7.62x39 (I don't know about other calibers).
Trigger in the Rem is long and creapy. A bit heavier than the Handi.
Lockup on both is tight. Needs to be looser on the Rem, but that will come with time.
There are folks that get GREAT accuracy with the Handi. A good part of that is tuning the for-end pressure/fit. Not possible easily with the Rem as there is a spring latch that holds the fore-end on. It's a game that requires some experimentation.
Rifling in the Rem is 4 groove, deep, a bit cruder than the Handi which is smoother and much shinier.
Muzzle crown on the Remington has about a 45 degree chamfer - a bit steep, but protective.
In general the Handi is machined more carefully, where you can see the characteristic roughness (except for the outside finish) of Russian do-the-minimum when it comes to manufacturing.
Sample of ONE of each. FWIW, YMMV.