Poor 3456a! See older discussions on eevblog for pros and cons.
As alm suggests, if you're a hobbyist, the 3456a will give you the same accuracy for VDC and ohms as the 34401a but at a slower reading rate, but much more user serviceable. The VAC is fairly mundane and it has no amp range.
Working uncalibrated units sell for $30-200 on eBay, versus $600-1000 for the 34401a, which is still in production. Abuse aside, the typical, if not, uncommon failure of 3456a over time is a PSU electrolytic cap, it will give error -4 on self test. Avoid the 2015Axxxxx serial numbers if you can, because the earliest run of them had defective eproms that have lost data with age [ any pic of the 2015Axxxxx series rear case will show a fan cage, which was removed in the later versions.] Fewer parts in the 3456a are unobtanium compared to the 33401a [ but you can send it back to Agilent for repairs.] If you need more than just high accuracy VDC and ohms, clearly look elsewhere. I paid $50 x 2, $100, and a calibrated one for $150, for 4 units; 3 years later one died with the -4 error and I'm in the process of replacing the cap.
Don't forget the Keithley 2000. Avoid the Keithley 2100, it was an outsourced design with limited support/documentation and some annoying firmware bugs that were never fixed as far as I know.
Don't mess around with the old hp 3456. They go cheap on ebay but are big and bulky and very old.
Very old or very well aged? 
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