A Leaked User Agent Code from Verizon website shows that the Verizon's Galaxy S3 version will have a Dual-core Snapdragon S4 chip along with LTE support, 720p Display. This was confirmed before by a Samsung Executive, he said that the Galaxy S3 will have two versions and sadly the US will a Dual-core version. Today if we combine the Code from Verizon (Photo below) with the Samsung Exec info we can confirm this info.

The User Agent leaked code from Verizon shows a handset with the model number SCH-I535 with a 720p display and powered by Android 4.0 ICS. Under the hood is the Qualcomm MSM8960 processor which is the Snapdragon S4. The model number seems to fit in with traditional model numbers used by Verizon for Samsung branded smartphones such as the Samsung GALAXY Nexus (SCH-I515), the Samsung Droid Charge (SCH-I510) and the Samsung Fascinate (SCH-I500).

Why Samsung will use S4 on US version ?

The International version of the S3 will have a Quad-core Exynos 4 CPU, Samsung used S4 CPU on the US version because Exynos 4 doesn't support LTE connectivity, but the S4 support LTE which will give verizon users an amazing 48Mpbs data connection speed faster than the 3G 21.1Mpbs.