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First of all, this is a very subjective topic. A, B and C class office buildings are general categorizations to denote the overall quality of office buildings.
A premier, first class office building. This category also sub-categorizes buildings to AAA, AA and A minus categories.
Commercial real estate agents and landlords would primarily agree that the degradation from AAA down to A minus is age related. When new towers are constructed and are at the top of the building food chain, older generation buildings cannot truly compare, so over time a AAA will downgrade to AA and then down to A or A minus.
While trophy buildings built in the 1970's or 1980's are still prominent business addresses, they do not carry the same prestige as the most modern buildings built today. This is especially true since the new buildings are incorporating great green technologies to keep operating costs low.
The criteria used to determine an A class building are:
3. Building size
4. Floor plate size
5. Tenant mix
6. Building systems - elevators, mechanical, HVAC, electrical
Most building owners tend to overplay their building classes - for instance on a space tour, if they call their building an A minus, most real estate brokers would deem the building to be a B or B minus.
Many B class buildings are just very old A class buildings. They have degraded enough over time to drop down to B status.
They tend to be utilitarian and practical but also very boring with nothing particularly special in the 8 criteria above.
While many of the aesthetics and systems can be renovated or replaced, building size, floor plate and location cannot.
The most common feature of a B class building would be a smaller floor plate size as the trend for A class buildings has been to increase the floor size, while older, B class buildings were frequently built with smaller floor sizes.
These are really old buildings - typically in the range of 50+ years old.
Many turn of the century buildings were built with very small floor plates, small elevators and small washrooms. They trade at a much lower net rental rate and do not allow companies to grow too much due to the small floor size. They are typically occupied by many small and start up companies, due to the small unit sizes, and reduced net rental rates.
Follow up reading: https://en.wikipedia.org/wiki/Office#Grading