Bangladesh is the latest victim of a natural disaster in which Islamists, including groups designated by the U.S. as terrorists, already have a social assistance infrastructure. The death toll from the Bangladesh cyclone has topped 1,100 as of this post and will climb further (updated at 2:20 pm ET). Bangladesh Islamist groups such as Hizbut Tahrir, Islami Oikya Andolon, Chhatra Mukti Andolon, Islami Shasantantra Andolon, and the deadly and dangerous Harkat-ul-Jihad-al-Islam (which uses mobile phone technology for triggering IEDs) will no doubt provide considerable funds to assist the victims and enhance goodwill among the populaceThe United States is offering aid but the long term goodwill that we could gain as being a responsible neighbor may be mitigated by both the delay, and the end channel distribution that the United States does not always control. Distribution and visible presence may be enhanced as the US Navy had a carrier group exercising in the Bay of Bengal in late September, so it could perform the same type of high visibility role that US amphibious ships perfomed in the tsunami relief effort.
The US due to the state's ability to marshal and then distribute massive quantities of resources will be able to send more over a medium time frame then any of the Islamist groups on the ground. However the loose network of groups have the advantage of being the first source of aid at probably the highest point of need, and being able to direct that aid because they live in the same locations... so as an empirical question, who gets further ahead in building goodwill and soft power support --- the first responders or the systemic infrastructure responders?