Is "peckish" less common in American English than other varieties?

Solution 1:

Yes, the informal expression peckish, meaning hungry, appears to be mainly used in BrE and AuE:

According to GDoS the term peckish dates back to the 18th century and the usage examples they provide are mainly from AuE and BrE. Peckish derives from peck, (16th C.) to eat (of a bird).

peckish: (also pecky) hungry:

1965 [UK] E. Bond Saved Scene ii: Still pecky? [...] There’s a bit’a choclit left. ’Ere.

1971 [UK] N. Armfelt Catching Up 204: I’m peckish myself.

1985 [Aus] R.G. Barrett You Wouldn’t Be Dead for Quids (1989) 47: Feeling a bit peckish now he [...] threw a T-bone [...] under the griller.

1989 [UK] (con. 1950s–60s) in G. Tremlett Little Legs 29: You come back a bit peckish.

1998 [Aus] R.G. Barrett Mud Crab Boogie (2013) [ebook] ‘Why don’t we order some food [...] I’m feeling a bit peckish’.

1999 [UK] (con. 1979–80) A. Wheatle Brixton Rock (2004) 27: I was feeling a bit peckish, so I thought I’d start dinner early.

2001 [UK] M. Coles Bible in Cockney 70: Did you never read about David when he was peckish and needed something to eat?

The term is mainly BrE according to the American Heritage Dictionary:

Peckish:

  1. (Chiefly British) Somewhat hungry.

and on the usage of peckish Vocabulary.com notes that:

While the informal word peckish is more common in the UK, most people in North America will know what you mean if you say, "I'm feeling a little peckish— should we make some popcorn?" Some people wake up in the morning feeling peckish, while others don't feel like eating for a few hours.

Solution 2:

According to Google NGrams the word is in the same order of magnitude in American and British English.

Actually, that's not true. Google Books Ngram Viewer does not show that they get the same amount of use.

A query that separates the US corpus from the UK corpus shows that peckish is almost twice as common in print in the UK as it is in the US:

US peckish versus UK peckish