Forum Moderators: rogerd
I would try both (assuming Invision is free - used to be, don't know about now....) and see which fits YOU - your method of work, what you like in board-ware, the types of customizations you want/will use, ease of installation, etc.
Hence, if you pay for Invision, you can count on some level of support if you run into problems. With phpBB, you'll have to rely on the support forums or contract for support separately. The phpBB community is very large and enthusiastic, though, so finding answers to common questions shouldn't be difficult.
Beyond that difference, I'd recommend you make a list of "must have" features, and see which board has more of them. Note that while both open source and commercial software often have "hacks" available to add features, if you have to install MANY hacks to get what you need conflicts can occur. Hence, I'd recommend choosing the software that does all, or almost all, of what you need "out of the box". (I guess software boxes are becoming less common these days... :))
Invision is still free, although I must admit they have made it a bit harder to find on their website, but I downloaded and installed it with little problem. I have hit one problem since though, which I'm waiting for a reply to it on the helpers forum - I'm considering registering. Their registration price is quite reasonable - $69.95, about £40 for one year.
I must admit I never did install and appraise phpBB, largely because I was upgrading my exisitng forum, running wwwboard, and wanted to get the new one up ASAP - the old one was attracting huge amounts of spam. The price you pay for running an unrestricted forum I suppose, and why I needed IPB or something similar fast!
I'd still vote for it - It's quirky, and you'll find their own support forums as useful as an ice cream in a swimming pool, but with the other forum and a bit of intuituion and work it's quite good.