The SCR-536 was much lower power, about 20mW RF emission, vs about 300mW for the SCR-300. While you can find the ranges of both given as 3 miles, this is a typical range under typical operating conditions in the field for the SCR-300, and the longest range under ideal conditions (e.g., over open water) for the SCR-536. Under typical operating conditions, the SCR-536 usually had a range of about 1 mile (or a quarter of a mile, depending on the source), and in poor conditions, sometimes only 100 feet.

While the SCR-300 had a much higher capacity (and much heavier) battery, the higher power used this higher capacity in about the same time. With the BA-70 battery (15lbs), the SCR-300 could operate for about 24 hours. while the SCR-536 with its rather more petite 1.15lb battery also managed about 24 hours. (The SCR-300 could also use the 9lb BA-80, for about 12-15 hours of operation.)

The SCR-300 is a clear winner in terms of range, and the SRC-536 is a clear winner in terms of portability.

This website has a copy of a US army radio equipment directory published 1944. The page for the SCR-536 (handheld) lists its range as 1.5 miles, while the page for the SCR-300 (backpack) lists its range as 3-5 miles. Not a huge difference, but the SCR-300 is definitely longer ranged. The manual also lists the power output: .027 watts for the SCR-536 vs 1 watt for the SCR-300.

The SCR-536 handheld unit was designed to be a tactical radio, issued at the platoon level to infantry units, each rifle platoon would have one, the company command unit would have one, and the company heavy weapons platoon usually was issued two. These six radios would typically be set to a common frequency and used as a company net. The SCR-300 backpack radio was intended to be used at a slightly higher level, with rifle companies having one each, that they could use to communicate with their battalion or higher level commanders.

It is significant that the SCR-536 was amplitude modulated (AM) while the SCR-300 was frequency modulated (FM). The disadvantage of AM modulation is that it is subject to bursts of static caused by broadband electromagnetic noise. The advantage is the circuitry is simpler, which lends itself to smaller total size compared to a FM unit. The most common source of broadband noise in WW2 was gasoline powered internal combustion engines; every time a cylinder fires in one of these engines the electrical spark generated by the spark plug generates a burst of broadband EM noise. Thus the army considered AM radios unsuitable for use in and around vehicles (all US army vehicles were gas powered in WW2). The AM handheld units were considered suitable for rifle units that had few if any vehicles, but the higher up the command chain you went, the more likely the commander was riding in a vehicle, which made FM radios more suitable when you got above company level. US tank and artillery units all used vehicle mounted FM radios, only the infantry used AM at the tactical level.