By the time the data reaches your PC via the USB/RS232 interface, the resolution and accuracy won't be any good. At the end of the day, without dedicated equipment, it is better to stay with NTP.
From this GPS synchronization tutorial
There are many cheap GPS receivers available in the market. Most of
them use either an RS232, or USB connection to send their information
to the attached computer. Although the clock inside the receiver
itself runs with an accuracy of some nanoseconds, the transfer of the
data to the computer causes such a large delay, that in practice it is
not possible to synchronize the clock of the local computer with that
signal with an accuracy of better than a handful of milliseconds. That
kind of accuracy can also be obtained by connecting to a freely
available NTP time server over the internet. Only GPS devices which
have a special fast and accurate synchronization method with the
computer can be used as a time synchronization device. The most
expensive and accurate way to do this is to use a GPS receiver which
fits in a local PCI or PCIex slot of the computer. But these cards are
very expensive and not widely available. The other solution is to use
the slow and inaccurate RS232 or USB interface to send general data
and do the time synchronization with a pulse.
As @dfc correctly points out, RS232 with PPS does the job. However, the device has to support it.
On most GPS devices with pulse capability, the pulse is sent once
every second, starting at the beginning of every new second. This is
why these GPS devices are often referred to as GPS with PPS, for pulse
per second.
Unfortunately there are not a large number of GPS receivers which have
the extra PPS output. I am using Garmin GPS receivers in Kazakhstan
for my tourism activities and I have therefore first looked at the
available devices from this manufacturer. Currently there are two
Garmin GPS receivers which may be used with a direct connection with a
computer: the Garmin GPS 16x LVS and the Garmin GPS 18x LVC. They both
work on a supply voltage of +5 Volt which is directly available from a
computer, they both send the general data in NMEA protocol over an
RS232 interface and they both have a PPS output.