The random private ATM's tend to have a limit of around 400 shek. Banks generally don't have that limit and I never had an issue taking out the max
Private ATMs are also more likely to charge a fee which may not be reimbursed by your bank. Bank ATMs also have limits. Using my Cap360 ATM card I have been able to get only up to 1,000 shekels at one certain location of Bank Hapoalim, around 2,000 at another, and at Bank Leumi I've done my daily $1,000 limit in one shot (close to 4,000 shekels).