Based on necessity the visitors coming throught mobile devices can be targeted two ways viz via responsive websites or by building separate mobile sites.
Separate mobile sites can be handy if we don’t want to show all the website to the user. Just if a website have loads and loads of data to show and not all the information for the visitors are useful then making a separate mobile site can be better option.
Mobile sites are generally the subset of the main site. The advantage of doing this will be the data will be loaded faster and we can target for the appropriate call of action.
My personal preference Mobile Website Development is Jquery Mobile.