If you are not reloading, then there is little difference to you. Some berdan primers are corrosive, but a quick patch or two when you are done shooting would solve that problem too. IIRC there are no corrosive boxer primed cartridges.
If you are reloading, then you need to stay away from anything berdan primed. You simply can't get them anymore, and they are not interchangable with boxer primers.
Having said that, You can convert a berdan primed case to boxer, but it is strictly not for greenhorns. I have converted a few. There is no reason whatsoever to do so other than to say "I can do it".
I keep some steel, berdan primed cases around. Why? you never know when you might need them.