This could be due to the amount of income received per pay period. Withholdings are also based on the amount of income as well as other factors and reflect tax brackets. If you income is lower on the new job, it may reflect a decreased tax rate therefore, less taxes being withheld.
Also, if you have a regular Retirement plan (not a Roth) that you are now contributing to, it will reduce your taxable income which affects your tax bracket.
Here is a great TurboTax tool to assist with calculating withholding below:
https://turbotax.intuit.com/tax-tools/calculators/w4/
