If you have an old DMM to compare it too, you can do some basic tests, but if you don't have one, your readings won't have any reference point, whether the reference is better or worse. Using both DMM alternately compare:
Measure a DC battery to the maximum number of digits
With usual care, Measure the AC main voltage, maximum number of digits
Measure its frequency
Measure any resistor, already at room temperature
Measure the current through the resistor, using the DC battery you have above. Is there any difference between what is measured and what should be using ohms law?
If possible and being extra careful, measure the AC current
If you have a function generator measure sine waves up to the rated frequency, what is the frequency response. Compare both DMMs to test the TRMS functions. If you have an oscilloscope, compare the RMS reading against the Vpp appearance. If you have a scope, compare the readings against a square wave and note the TRMS reading against Vpp.
If you have any capacitors at hand, measure those.
These are at least, some of the essential basic electrical measurements. Without knowing who has better and realiable specs, the least you'll know is one meter is different from the other. If the Agilent comes with a calibration certificate, then we know its the better meter, and so now it tests how different your other DMM is compared to a NIST traceable one.
Re: the request for performance tests...
I would like to ask for testing suggestions since in my world of AC power there are no cut and dry standards to compare and I don't usually think in those terms. I can compare 50 DMMs and still never know which is showing me the most accurate reading of the mains voltage. The same holds true for the typical resistance measurements I make. Today I installed floor heat and had to verify that the cable and temperature sensor met specs. The cable is supposed to read ~37.5 Ohms while the sensor can read from 8k to 12k Ohms at 20-30 degrees celsius and of course the ambient temp was 18.6 and my reading was outside the published values
So any suggestions would be welcome!