Most of programs use the same parameter file. See BLUPF90 manual for details on this file. Some programs have restrictions on parameter files and some programs use optional parameters. Details on these can be find in Readme* files in directories of specific programs.
Below are comments on specific programs and descriptions of some options.
BLUPF90 calculates BLUP with 3 solvers. PCG is the default solver and is usually the fastest one. There is an option in the PCG module to use the block preconditioner at a cost of higher memory requirements. Solving with SOR would require less memory but usually would converge slower. In pathological cases SOR may be more reliable as it does not have an error accumulation properties of PCG. FSPAK is usually the most accurate method and usually uses the most memory. With SOR, one can convert the program to using single precision (rh=r4) and use only half of memory.
REMLF90 uses EM REML. For most problems it is the most reliable algorithm but can take hundreds of rounds of iteration. REMLF90 was found to have problems converging with random regression models. In this case, using parameter files that are too large than too small usually helps.
AIREMLF90 usually converges much faster but sometimes does not converge. Very slow convergence usually indicates that the model is over parameterized and there is insufficient information to estimate some variances.
GIBBSF90 is a simple Gibbs sampler. It is very easy to change but is slow as it recreates LHS and RHS every round. Use postgibbsf90 to analyzes samples from this and other Gibbs samplers. In practical cases, results from Gibbs samplers and REML are similar. One would one or the other based on computing feasibility. If there are large differences beyond sampling errors, this indicates problems usually with the Gibbs sampler. Try longer chains or different priors.
Gibbs samplers may be slow to achieve convergence if initial values are far away from those at convergence, e.g., 100 times too low or too high. Before using more complicated models, Karin Meyer advocates using a series of simpler models.
GIBBS1F90 is usually much faster than GIBBSF90 because LHS is stored only once and separate from relationship matrices. Successful analyses were made with over 20 traits. However, if models are different per trait, the lines due to effects need to be modified. Also, with too many differences in models among traits, the program becomes increasingly slower.
GIBBS2F90 adds joint sampling of correlated effects. This results in faster mixing with random regression and maternal models. GIBBS2F90 is usually the program of choice for Gibbs samplers.
GIBBS3F90 adds estimation of heterogeneous residual covariances in classes. The computing costs usually increase with the number of classes.