Rommel in his reports said that American artillery was superior to German in the Italian campaign. What made it superior?

US industrial capacity gave them all kinds of advantages. In no particular order: The US had more spotter planes (the Germans had a good but expensive plane in the form of the Fi 156). The US basically built new weapons for everyone so it was able to standardize on a few designs making things like ammo supply a lot easier (German units frequently were formed using captured/foreign equipment). Ammo supply (or lack thereof) was a chronic issue for the Germans. The US had enough trucks to fully motorize its units (the Germans were still using horses). This gave US artillery both significant maneuverability advantage, as well as making it a lot easier to keep guns supplied (One side fact: When the Sixth Army was encircled in Stalingrad, the artillery horses were outside the encirclement area, which would have severely complicated a breakout attempt if one was made). The US gave everyone and their uncle a radio, and trained NCOs in the basics of calling in a fire request.

All of these things made significant differences. However the biggest factor was the absurd amount of math that the US pre-calculated.

The US system starts on the US mainland, where the Ballistics Research Laboratory at Aberdeen compiled ballistic data for the US guns under all sorts of conditions. This data was passed to Fort Sill (home of the US Artillery School) and the Frankford Arsenal, where it was digested (involving a whole lot of math) into a series of firing tables. It's really hard to give an idea of how much work this involved, but the end result was a filing cabinet full of tables.
US units 'in the field' were provided with extensive maps of the area. In the event that artillery units were not supplied with maps they were also trained to generate their own on the same scale that the supplied maps would use.
When a fire mission was called in the fire direction center would pull out the appropriate fire control table for the current conditions and use a simple analog computer (slide rule) along with the map to determine how to lay the guns. This was a fairly quick process that only took a few minutes. The low level FDCs were monitored by higher level commands so if needed this process could be repeated by other batteries and a unit could get support from multiple sources.
All this means that it was theoretically possible for a US unit to call in fire from every artillery unit within range in just a few minutes. While not Italy a pretty classic example of this was Hill #314 in the Battle of Mortain where a US infantry battalion (or perhaps less? sources seem to vary) was able to hold the hill (deny the use of a road it overlooked) against the better part of a German division thanks to rapidly responding artillery support.

The Germans on the other hand were not able to do all of this pre-calculation, and as a result their equivalent to the FDC had to spend significantly longer 'doing the math' before a fire could be started, which stretched the 'reaction time' to tens of minutes.

When you're trying to bust-up a counter attack or hit a target of opportunity the difference between a 3 minute response and a 15 minute response is pretty significant.