Question is similar as "webhosting or vps to host a site". Depend from your needs, guess. VPS is more flexible and if you also need few bounchers, bots or services... it would be better choice.
You also mentioned BROWSER based chat, so you need place for your web browser script (vps again..). I can see only advantages in vps case unless there's problem to manage it - in this case IRCd server set up by irc shell provider would be better choice (however you still need a place to put web browser chat script).