Equal area map projections: Lambert azimuthal or Albers conic?

It depends also on the location you want to map which you did not specify.

From ArcGIS Help, on Albers Equal Area Conic:

Limitations

Best results for regions predominantly east–west in orientation and located in >the middle latitudes. Total range in latitude from north to south should not >exceed 30–35°. No limitations on the east–west range.

Uses and applications

Used for small regions or countries but not for continents.

Used for the conterminous United States, normally using 29°30' and 45°30' as the two standard parallels. For this projection, the maximum scale distortion for the 48 states is 1.25 percent.

One method to calculate the standard parallels is by determining the range in latitude in degrees north to south and dividing this range by six. The "one-sixth rule" places the first standard parallel at one-sixth the range above the southern boundary and the second standard parallel minus one-sixth the range below the northern limit. There are other possible approaches.

ArcGIS Help for Lamert Azimuthal:

Limitations

The data must be less than a hemisphere in extent. The software cannot process any area more than 90° from the central point.

Uses and applications

• Population density (area).
• Political boundaries (area).
• Oceanic mapping for energy, minerals, geology, and tectonics (direction).
• This projection can handle large areas; thus it is used for displaying entire continents and polar regions.
• Equatorial aspect: Africa, Southeast Asia, Australia, the Caribbean, and Central America.
• Oblique aspect: North America, Europe, and Asia.