There are a few things you could do to improve accuracy.
- Make up a custom board (itself not particularly hard) with a crystal rather than a resonator for higher accuracy (and perhaps get a crystal with good specs)
- Include a temperature sensor
- If measurement shows that time drifts depending on temperature, then if you know the temperature (from the sensor) you could compensate to some degree (pun not intended)
You could consider something like the ChronoDot:http://www.adafruit.com/products/255
According to the documentation:
This makes the ChronoDot very well suited for time critical applications that cannot be regularly synchronized to an external clock.
I don't know if you can get microsecond accuracy from it, but the SQW signal might achieve that.
It might be worth experimenting with. However I honestly don't know how accurate that would be compared to maintaining your own count of clock ticks using one of the timers.
My experiments will be done within half an hour. So, I have to check how much it drifts within that time.
If they both start at the same temperature, and are synced together, and the test is conducted 30 minutes later, the drift due to temperature would be negligible I would have thought. Especially if you transport (or store) them in a thermal insulating box to minimize changes (eg. from the car trip).
As for inherent inaccuracies in the clocks, a quick test over an hour where it reports the timer counter periodically should show if one is drifting with respect to the other.