BigDecimal equals() versus compareTo()

The answer is in the JavaDoc of the equals() method:

Unlike compareTo, this method considers two BigDecimal objects equal only if they are equal in value and scale (thus 2.0 is not equal to 2.00 when compared by this method).

In other words: equals() checks if the BigDecimal objects are exactly the same in every aspect. compareTo() "only" compares their numeric value.

As to why equals() behaves this way, this has been answered in this SO question.

I believe that the correct answer would be to make the two numbers (BigDecimals), have the same scale, then we can decide about their equality. For example, are these two numbers equal?

1.00001 and 1.00002

Well, it depends on the scale. On the scale 5 (5 decimal points), no they are not the same. but on smaller decimal precisions (scale 4 and lower) they are considered equal. So I suggest make the scale of the two numbers equal and then compare them.

I see that BigDecimal has an inflate() method on equals() method. What does inflate() do actually?

Basically, inflate() calls BigInteger.valueOf(intCompact) if necessary, i.e. it creates the unscaled value that is stored as a BigInteger from long intCompact. If you don't need that BigInteger and the unscaled value fits into a long BigDecimal seems to try to save space as long as possible.