It seems you are asking this question from the position of the BUYER. If my assessment is correct I have a different answer than above.
Historic tax credits benefit the developer, not a purchaser. If you purchase a home or condo that was renovated as a tax credit project, those tax credits benefit the developer, not you, unless you ARE the owner/developer and this is a tax credit renovation of your own personal residence. Tax credits are a dollar for dollar reduction in personal - or corporate - income tax liability. There are two types of historic renovation tax credits available in Virginia: (1) federal tax credits, which credit the developer with 20% of the qualified rehabilitation expenses ("QREs"), but only for income-producing property; and (2) Virginia state tax credits, which credit the developer 25% of the QREs for any approved renovation project, even a personal residence. If the project is a qualified income-producing project in Virginia, it may qualify for BOTH the federal and state credits, meaning 45% of the QREs as a direct bottom line tax credit.
A tax abatement is a completely different animal and DOES benefit a purchaser. The program works like this: The renovating party, be it developer or home owner, applies for the tax abatement with the City of Richmond Assessor's Office. The City assessor sends someone to evaluate the value of the property BEFORE renovation. That before renovation value is the "base value," or X. After renovation the Assessor's Office sends someone back and determines the after-renovated value of the property, or Y. The difference between Y and X is the "abated amount" and that value, the value added to the property, is exempt from real estate taxes for 7 years in total, and comes back in 25% each year 8-10, until Year 11 when the full assessed value is subject to real estate taxes. This can be a significant financial advantage to a home owner and save tens of thousands of dollars over the 10 year abatement period. An abatement also runs with the property and is transferrable upon sale, if there is any remaining time left.
These programs are technical and this is just a general overview. Consult an expert for detailed guidance. I also have some more detailed analysis on my bog, the address of which is below. Good luck!