[PERFORM] index of only not null, use function index?

I need to be able to quickly find rows where a column is not null (only a
small percent of the rows will have that column not null).

Should I do:

CREATE INDEX ON table ((col IS NOT NULL)) WHERE col IS NOT NULL

or:

CREATE INDEX ON table (col) WHERE col IS NOT NULL

I'm thinking the first index will make a smaller, simpler, index since I
don't actually need to index the value of the column. But are there any
drawbacks I may not be aware of? Or perhaps there are no actual benefits?

      -Ariel