We present a quantitative classification scheme for carbon and oxygen sequence Wolf-Rayet stars. Our scheme uses new high-quality optical AAT and INT observations of 20 stars for which we provide narrow-band photometry and estimates of interstellar reddenings. In increasing order of excitation, our spectral classes range from WC11 to WC4 for Wolf-Rayet stars with a dominant carbon line visual spectrum, and subsequently from WO4 to WO1 for those with predominantly oxygen lines. We refine existing WC and WO schemes to incorporate stars with higher and lower excitation spectral features. Both massive stars and central stars of planetary nebulae (CSPNe) can be classified with the unified system. We have found no criterion that cleanly separates spectra of the two types of star, including elemental abundances (C/O or C/He). However, CSPNe show a wider range of line strength and width than massive stars in the same ionization subclass. Systematically lower FWHM(Civ lambda5808) values are observed from WO-type CSPNe than from massive WO stars. For WC4-11 stars, our primary diagnostic is the equivalent width or line flux ratio Civ lambdalambda5801-12/Ciiilambda5696. We extend the use of this as the principal criterion throughout the WC sequence, with few reclassifications necessary relative to Smith, Shara & Moffat. For WO stars, Ciii is absent and our new criteria, using primarily oxygen lines, take over smoothly. We define subclasses WO4-1, using Ovi lambdalambda3811-34/Ov lambda5590 as our primary diagnostic. The continuation in spectral sequence from WC to WO is used to indicate that the sequence is a result primarily of excitation effects, rather than significant abundance differences. Our scheme allows us to confirm that massive stars and CSPNe are differently distributed over the subclasses. Around 3/5 of massive WC stars lie within the range WC5-8, while <=1/5 of CSPNe are found within these spectral types. Stars within both the highest (WO1) and lowest (WC10-11) excitation spectral classes are unique to CSPNe. A WC classification for the hot RCrB star V348 Sgr is excluded (previously [WC12]) since both Ciii lambda5696 and Civ lambda5808 are absent in its optical spectrum. Additional criteria allow us to distinguish between WC-type, `weak emission line' CSPNe, and O stars, allowing us to reclassify the central star of IRAS 21282+5050 (previously [WC11]) as an O star.