Given the choice between the two, I would say that it depends on who your customers are. If they are within the US, I would definitely choose to pursue the PE. If they are international, the path to becoming a Chartered Engineer MAY be less daunting (depending on where you are and how much of a presence IChemE has there).
PE registration is administered state by state within the US. The good news is that the NCEES (National Council of Examiners for Engineering and Surveying) is an organization comprised of the 69 state (and territorial) Boards that regulate engineering within each state and it offers excellent information regarding registration requirements. See ncees.org for details. They have jointly developed Model Law in an attempt to harmonize state requirements, and also offer the Records Program, which facilitates multi-state registration. Admittedly, it is difficult to overcome the education requirement for an engineering undergraduate degree from programs accredited by ABET/EIC, but I suppose that it happens in rare exceptions.
The best way to answer you is to refer you to the NCEES web page www.ncees.org .
Check out the AIChE Academy PE exam preparation course. It is a fairly recent addition, and has been supported by volunteer members of the Licensing and Professional Development Committee of AIChE.