Any SE advantage to CSS over HTML tag coding?

A client asked a question today which I could not answer honestly. He came to us for a makeover and update on his web site. It is a old site which uses generic HTML tags and very few style sheet definitions. Client is old school and likes it that way "because its easier for me to understand and edit". Last developer charged him about $2k and gave back a crapola 600k "kitchen-sink" style sheet which made him blow his stack. He asked what search engine advantage there is for using a linked CSS sheet and asked for us to split out the charges for converting all tags to style definitions. I babbled some generic comments like 'current standards' and 'modernization' and 'efficiency, convenience and caching' as I realized that I did not have a conclusive (i.e. honest) answer for him.

Is there a search engine advantage to using linked CSS style sheets instead of in-line HTML tags? Is there any advantage to using a single site-wide style sheet over 3-4 different sheets specific to page sets?

Hand holding sincerely appreciated on this one!