The US does not identify any of its ally states (at government level) as state sponsors of terrorism. Iraq for example was removed in 2004, following the US invasion. The current US list of state sponsors of terrorism is actually pretty short (as of 2017): besides Iran, only North Korea, Sudan and Syria (Assad's regime) are on it. The official reports don't seem to put a lot of effort in arguing which of these is the biggest, except perhaps as a threat-level to US interests:
In its annual “Country Reports on Terrorism” released Wednesday, the State Department said Iran was the planet’s “foremost” state sponsor of terrorism in 2016, a dubious distinction the country has held for many years. It said Iran was firm in its backing of anti-Israel groups as well as proxies that have destabilized already devastating conflicts in Iraq, Syria and Yemen. It also said Iran continued to recruit in Afghanistan and Pakistan for Shiite militia members to fight in Syria and Iraq. And, it said Iranian support for Lebanon’s Hezbollah movement was unchanged. [...]
“Iran remained the foremost state sponsor of terrorism in 2016 as groups supported by Iran maintained their capability to threaten U.S. interests and allies,” said the report [...]
Interestingly, the 2017 edition of the report lacks the "strategic assessment" chapter where the "foremost" declaration was usually made. The 2016 edition had this reasoning for Iran the being "foremost":
Iran remained the foremost state sponsor of terrorism in 2016 as groups supported by Iran maintained their capability to threaten U.S. interests and allies. The Iranian Islamic Revolutionary Guard Corps – Qods Force, along with Iranian partners, allies, and proxies, continued to play a destabilizing role in military conflicts in Iraq, Syria, and Yemen. Iran continued to recruit fighters from across the region to join Iranian affiliated Shia militia forces engaged in conflicts in Syria and Iraq, and has even offered a path to citizenship for those who heed this call. Hizballah continued to work closely with Iran in these conflict zones, playing a major role in supporting the Syria government’s efforts to maintain control and territory, and providing training and a range of other support for Iranian aligned groups in Iraq, Syria, and Yemen. Additionally, Hizballah continued to develop its long-term attack capabilities and infrastructure around the world.
In the 2017 edition this assessment was reworded and moved to the foreword:
Iran remained the world’s leading state sponsor of terrorism and continued to support attacks against Israel. It maintained its terrorist-related and destabilizing activities through the Islamic Revolutionary Guard Corps (IRGC) Qods Force and the Lebanon-based terrorist group Hizballah. Iran is responsible for intensifying multiple conflicts and undermining the legitimate governments of, and U.S. interests in, Afghanistan, Bahrain, Iraq, Lebanon, and Yemen. In particular, Iran and Hizballah are emerging from the Syria conflict emboldened and with valuable battlefield experience that they seek to leverage across the globe. IRGC leader Qasem Soleimani recruited and deployed Shia militias from diverse ethnic groups across the Middle East and South Asia to fight in defense of the Assad dictatorship in Syria. Beyond the Middle East, Iran and its terrorist affiliates and proxies posed a significant threat and demonstrated a near-global terrorist reach. Notably, in June 2017, the FBI arrested two suspected Hizballah operatives in Michigan and New York who allegedly were conducting surveillance and intelligence gathering on behalf of the organization, including in the United States.
ISIS etc. are deemed non-state actors.
Since 2016 at least Pakistan is listed as a "safe haven" for terrorists, but not outright sponsor of terrorism. The latter list of "safe haven" countries, which I'm not sure when it first appeared, is actually pretty long. In the 2017 edition it includes Venezuela, Colombia, Afghanistan, Yemen, Libya, Lebanon, Iraq, Egypt, "The Southern Philippines", "The Sulu/Sulawesi Seas Littoral", "The Trans-Sahara", "The Lake Chad Region", and Somalia.
Also, some people, including Trump himself before the election have been implicitly critical of the official categorization, e.g.:
In his 2015 book, ‘Time to Get Tough,’ which was published ahead of the presidential election, Trump wrote: “Then look at Saudi Arabia. It is the world’s biggest funder of terrorism. Saudi Arabia funnels our petrodollars – our very own money – to fund the terrorists that seek to destroy our people, while the Saudis rely on us to protect them.”