Raster charts are bitmapped - ie pixels (small squares or picture elements) of fixed colours. When you zoom in on them the image quality degrades. If you zoom in a long way they become difficult or impossible to read. However, most chart makers produce charts of good enough quality, so this doesn't really become a problem in normal use.
Vector charts are constructed differently - they always display at full screen resolution regardless of the zoom level and so are better quality.
The choice probably depends on which chart plotting software you have (or want to get). Some software is able to display both raster and vector charts.
A major difference is that in a classic raster chart you are not able to switch on/off certain elements like land roads, depth contours, buoys. The program that makes use of the chart doesn't really understand the chart, it could also be a photograph of Paris Hilton in a orange suit.
A vector chart is actually created by the program on your plotter to to display on the screen, based on a huge number of coordinates stored on a CD or cartridge. For every element the program 'knows' what it is i.e. part of a coastal line or a buoy. Because of this you can selectively switch things on and off.
You can combine the two by making the basic chart as a raster and all the points of interest (buoys, high buildings on the coastline, depth markings) as a vector point.
Many people prefer the looks of a raster chart because it resembles the paper chart more then a vector chart. However the advantages for a vector chart are tempting as well.
In general a raster chart takes up more space on a storage medium than a vector chart.
best way to view vector charts systems is as interactive. they are seamless, the detail can to a degree be selected by the operator, you can to a degree put marks / symbols on the charts, and perhaps most useful you can easily incorporate tide data and in some systems weather data. this is all because every bit of info on them is turned into digital data and can therefore be manipulated by the processor.
raster charts are photocopies in effect. you can make your own raster charts by scanning paper charts and using a stitching programme to fit the piccies generated together. or you can buy the equivalent of admiralty paper charts. the UKHO favour raster systems but I always got the impression this was because they were afraid that they would end up with court cases if they let joe public decide what detail the screen would show. as a result, everyone else has stolen a march on them because joe public seems to prefer vector.
Raster - yes are based on scans of paper charts / templates. Can be any form of graphic literally that can be read by calibration program. Some have taken it further by adding a companion data file ... eg BSB + KAP ...
Vector are based on Points, Polylines or Polygon areas. An image is traced with polyxxxx and saved in Polish format ... then worked on to produce layers which can have switch on / off capability and also some are only viewable at certain zoom levels.
The advantage of Vector is the non-pixellation of display especially text / data on screen. Raster will quickly lose clarity in text / data such as buoy info etc. as you zoom in closer. Vector will always be readable.
There are odd examples of raster that have overlays to assimilate Vector and give better display choice - but still zoom limitations occur.
It is probable that Vector will become the overall standard eventually and Raster will fade away as it gets overtaken rapidly.