FamilySearch have at last admitted that some of the records included in the International Genealogical Index (IGI) at the old FamilySearch site are NOT included in the datasets at the new site. Whilst there are many new datasets at the new site, including some images, a recent email to LostCousins member Ruth revealed that some IGI records have not been included because of copyright issues. In the circumstances my advice is to use both sites - each has a link to the other from its home page. You'll also benefit from the different search techniques.
Well yes - but go carefully. One of the problems with the IGI was that it contained information from family trees which contained errors - and in the past I have helped many people who had been led up the garden path by such wrong or misleading entries.It is clear that at least some of the "missing" entries were this unreliable ones.