REMOTE: Other than Wireless Testing, this is the default for all testing services.  The security tester never physically visits your site. Although a remote evaluation will not address "physical" attacks, it will ensure you have a measured level of security from remote threats.
ON-SITE: The security tester goes on-site on multiple occasions to perform local assessments in addition to remote assessments. Advantages to on-site testing is the ability to assess wireless/wired infrastructure, physical access attacks, more thorough social engineering attacks, etc.
On-site testing is certainly more effective as it helps protect you against local and remote attacks. However, if your organization is not concerned with the local attack vectors, then remote testing may be all you need.
Additional fees for On-Site Testing
In addition to the cost of the service you select, there is a two-part additional fee for on-site testing.  The first is the mileage fee of [text-blocks id="690" plain="1" myDesc="$x per mile from Y"].  The second part is the number of days needed and what the testing includes.  At minimum, this part of the fee is typically $200-400 per day.  Example: a small testing engagement in Dallas might be (275 miles x [text-blocks id="690" plain="1" myDesc="$x per mile from Y"]) + $350 = $1,175.  That is, $1,175 in travel expenses, in addition to the cost of the engagement itself.