They are basically the same but the second one is a bit more casual.

If you are "picking holes in something" then you are also "finding fault", but the reverse is not true. "Picking holes" occurs only when you are finding fault with someone's logic. I would say it is usually wrong to say "picking holes in my work". You can find fault or criticize someone's work, but you only pick holes in their work if their work is of a logical nature. If their work is to explain, then you can pick holes in their work. If they are a computer programmer, you can pick holes in their coding by pointing out their logical errors. However, if they are gardeners who have done a terrible job planting, you cannot pick holes in their work. You could, however, pick holes in their landscape plan.

Just a comment on phrase #2: Although "picking holes" pops up when I do a google search, it sounds more natural to me to say "poking holes in my work" or "picking apart my work"

I'll second Guide Dog Saint's answer. There's a big difference in the level of formality. And I'll concur with Jonathan also. You can only "pick holes in" arguments or logic, but you can "find fault with" a wide variety of actions, thoughts, states, etc.

It's the same.