小心眼 is more figurative than 小气。小气has more meanings,one of which is 小心眼 when it means somebody is easy to get angry or remember other people's misdeeds.
小气 is also used to describe a person when he/she is not generous. e.g. Though she is a millionaire, she doesn't want to give me a penny. She is very 小气。(You can't say 小心眼here)