Connectivity Issues

Any irc client can connect to any irc server, as that's the point of irc clients to begin with. Using a client means you get some added functionality over mibbit, a probably-sleeker interface and debatably an easier time of joining the irc (instead of having to open the browser tab each time and logging in through mibbit etc. which entails needing your browser to be open you just launch the client and bam).

As Agen mentioned this also has the advantage of allowing you to log IRC channels/user chats/whatnot to text files on your computer so you have records of what was said if you need 'em for whatever reason.