They are not that similar, to my mind at least. Cut down is about reducing the size of something. Boil down is about looking at the root cause or major issue of something

Hi,

They are very similar phrases and somewhat nuanced. They are similar but not interchangeable. I tend to use "cut down to" when speaking about shortening specific things/objects and insert that object into the phrase. For example:

“Can you cut the price down to $3”

“Can you cut your paragraph down to 100 words or less”

“Can you cut the time down to 20 minutes”

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I use “Boil down to” when reducing concepts and giving a summary. For example:

“Political fighting boils down to an unwillingness to compromise”

“How long it takes to learn boils down to how much time you spend studying”

“How long the job takes boils down to how hard you are willing to work”