Difference between cordic algorithm and table based methods for elementary functions computation
CORDIC uses small table to work, it calculates one bit at the time and being shift and add algorithm it is preferable when there are no multipliers available. Whenever multipliers are present, table based methods or power series are faster. Also one point worth notting - the scalling factor is also needed which sometimes is argument to use BKM, but this one is slower than CORDIC.

CORDIC is still used in x87 FPU, but nowadays Chebyshev polynomials are preferred way to compute special functions (or transcendental, but not elementary - this is rather bad name) (also do not consider Taylor here, it is very slow and works for small angles).

Drawbacks in both methods are increase in number of iterations and tables provided. Good to know how they work and grasp a piece of history, but not practical in software and not preferrable in hardware.