There is no objective criteria for comparing which piece of military hardware is "better". Less so when comparing military equipment between armies with vastly different doctrines and circumstances such as the US and Soviets. It's also a question of when? 1941? 1943? 1945?
What might be useful is a review of US and Soviet mortars in WW2 and how they were used.
US and Soviet mortars of WW2 were all based on the British Stokes and its refinement the French Brandt mle 27/31. They all used a fixed firing pin for simple operation, drop the shell in the tube and away it goes. They all determined their range by elevating the barrel (with one notable exception) and extra charges. They could be split into three pieces, the barrel, plate, and monopod, for easier transport. Their relatively light weight meant they could be carried by their crews right up to the front line if necessary in any terrain.
See Weapons 101 - How does a Mortar work? by Military History Visualized for more detail.
As we'll see, the US used mortars in their original intended role as quick, close artillery support for the infantry. The Soviets also used them in this role, but also made much heavier mortars as cost-effective traditional artillery.
The US used just three mortars during the war, the light 60mm M2, the medium 81mm M1, and the heavy 4.2" (107mm) M2. They all had some features in common. They were provided with various HE and smoke shells, including white phosphorus. They had various fuzes to choose from and good sights. Special shells could further increase the range. These are all extremely reliable, robust, long range, and accurate designs used through the war and after. They served the US army well in any terrain.
The US entered the war with just the 81mm M1 and its scaled down variant the 60 mm M2. These were smoothbore using fin-stabilized shells. In addition to HE and smoke, they also fired an illumination shell. Both used the excellent M4 sight. The M1 provided a rifle battalion with some integral artillery support. The scaled down M2 was for rifle companies.
In 1943 the US introduced the heavy M2 4.2 inch (107 mm) mortar to provide organic heavy mortar support to division. This was a rifled mortar, no fins required. Too big to be man portable, like the other mortars it could be broken down into three pieces luggable for short distances by a team of men, animals, or light vehicle. This gave the US army a heavy artillery option in even the roughest terrain of Sicily, Italy, and the Pacific. It was even fired off landing craft in support of landings.
In contrast to the US, the Soviets had problems with their light and medium designs. Eventually they focused on their excellent heavy 120mm mortar as well as developing a huge 160mm weapon. Soviet optics were generally inferior to the US.
At the lightest end, the Soviets began the war with a one-man 37mm mortar that doubled as a spade (?!). The idea was to give every Soviet infantryman a fire support weapon; most other countries went with rifle grenades instead. Lacking an aiming device, these were found to be ineffective and mostly for morale purposes. This weapon was quickly withdrawn from service.
Next the Soviets had a 50 mm mortar for company use. Unlike other mortars, its elevation was fixed. Range was determined by a gas management system. It was thought this would be more precise. In practice it was inefficient, cumbersome, and inaccurate. The 50mm projectile was too small to be useful. Several revisions failed to fix these shortcomings and the light mortar was abandoned. However the Soviet equipment problems meant it continued to be used as long as stocks allowed.
The 82mm mortar was nearly identical to the US 81mm M1 and also used as a battalion level support weapon. Tinkering with the design lead to the flawed 1941 model, and it's eventual correction in 1943.
The 107mm M1938 was derived from the 82mm mortar. It was designed to give mountain infantry divisions heavy artillery portable by pack animals and man-handled into position.
The 120mm-PM-38 was an upscaled 82mm mortar on a wheeled carriage. It was the heaviest artillery that could still be transported by men alone. It served at the regimental and battalion level. It's heavy shell, mobility and quick setup and tear down meant it could serve in a counter-battery role and hit-and-run attacks. It gave Soviet rifle units a significant punch. This was replaced with an improved 1943 model. It proved very popular post-war.
And finally, in 1943 the Soviets introduced a massive 160mm MT-13 mortar based on the 120mm. At 1170 kg with a 3 meter barrel firing a 40 kg shell, the barrel was so long and used as such high angles the crew could not reach the muzzle to drop the shell down, so it was made breach loading. It's large size meant it was not used in the traditional mortar role of quick infantry support, but more as a cheap way to manufacture heavy artillery.
Which is "better"? Despite what I said at the start, we can make some objective comparisons.
In a head to head comparison, the US 60mm M2 is a clearly superior weapon to the flawed and underpowered 50mm. Otherwise they were all basically copies of the same French design with only variations in size and quality.
Beyond that, we must to consider the needs of the US vs Soviet military to understand why the designs diverge. The US military had plenty of manufacturing capability safe behind and ocean to deliver artillery and attack aircraft to preform the traditional artillery roles. This left the mortar in the US army in its niche as a quick, close artillery support for the infantry. US mortars remained relatively small weapons, much bigger and you might was well call in artillery or an air strike.
In contrast the Soviets needed artillery and they needed it now. While the mortar was used to give the Soviet infantry punch, it also was a cost-effective way to supplement traditional artillery. Thus they grew in size and firepower, and dropped in mobility.