UK, Ireland /
Poles becoming British subjects [39]
As a Belgian citizen you probably wouldn't get any benefit from one unless you wanted to go to certain former British colonies and even then the passport thing only applies to a feW of them. Most countries have a list of nationalities who can get a visa on arrival, who dont need a visa or who are entitled to certain advantageous categories of visa. Citizens of the UK (and Belgium) usually do quite well out of this. So do Polish citizens (in comparison with, say, Nigerians) however the list doesn't always include Poland.
I have to travel quite a lot for work and it is quite convenient in some countries to sail through passport control while Russians, Americans, Chinese, Indians etc are queuing twenty-deep at chaotic visa booths with handfuls of photographs and forms and never the right amount of local currency.