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Both Breeding Advice and Strict Breeding Advice will compare the foal to both parents. BA allows foals that are slightly worse, as good as, or better to pass; SBA only allows foals as good as both parents or better than both parents to pass. SBA effectively runs the foals through a finer tooth comb. However, as you get closer to the breeding cap, fewer and fewer foals will pass SBA since there is less upside "better" range for the foals to fall into.

I also do benchmarking using comparison - so I'll test foals against the best in pasture from that year or the year prior (they can only be tested against the same sex, so if the best in pasture this year is a filly, I may have to compare my colts to an earlier best in pasture. Benchmarking gets expensive quickly though, so I'd really only recommend it when you're no longer struggling for hbs every month.

As Good As is an "about" figure - the as good as horse may be exactly the same as the comparison horse, slightly better, or slightly worse.

In my example above, all three colts were as good as their sire, but Gygax evidently has a slightly higher breeding score since Gygax is also as good as Atatraxis, but Mario and Nat One are worse than Atatraxis. You can use comparison testing to determine while horses are better for breeding, even if they paper the same.

For example, let use the example of fillies A, B, and C that are all blue papered and test Better than their red dam.

If you get the following three results from three tests:
A tests As Good As B
A tests Worse than C.
B tests As Good As C

Then you know the C is the best of the three, B is the second best, and A is the worst.
(A is worse than C. Because B is As Good As both of them, we know that B falls slightly above A but slightly below C.)

edited: I was suddenly overcome with self-doubt on how BA and SBA worked. Looked them up again and corrected them.

Thank you, both of you, I really appreciate your experience and insights :x