To be honest, there are a lot more mods available for anti-bot spam posting on phpBB than for Invision (mostly using captchas and similar human-poster auth types).
Invisionize and InvisionModding (two large IPB modding communities) were pretty devoid of answers beyond "Don't allow guest posting" when I was looking for help combatting our bot spam here and on AR. Of course, that's becoming more and more useless when you consider that spambots can actually register and validate for your forums nowadays, and it's getting worse.
There are many features, however, that make Invision highly recommendable over phpBB (the minimal-tweaking customization options, stability, security, and support are much better as expected for a commercial board) - but if spambots are your main consideration for switching, I wouldn't bother paying the money until Invision develops better support for those issues.
Of course, if you just want a smoother forum and someone to point the finger at and get angry with when technical issues happen, go for IPB :P
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