I dont think its a matter of "which forum" but rather its a matter of skill with coding and css.

There are many great forum softwares - SMF is one of my favs, but to get it to look like your current website will always require some manipulation of the forum's css. You could try to find a skin that closely matches, but there will always be compromise - better to get your hands dirty with CSS if the budget allows.

If you want to use your current website CSS in your forum, then you will need to include the CSS file in the head of your forum. Thats pretty simple to do usually, but you will still have styles that are unique to the forum that are not defined in your main CSS. So either way, you will need to do significant CSS edits.

There is one way to almost avoid this - use Joomla CSS with Fireboard. Fireboad is a 3rd party component that integrates with Joomla - its not a seperate package requiring a bridge of wrapper. It has an option where you can have it use the main joomla CSS styles. Although this sounds promising, I have found that you still need to tweak the css to get it looking perfect. Fireboard is full featured - so it has everything that the others have, with the current exception of user groups - you are stuck with the joomla acl.

Here is a recent example of Joomla with Fireboard and very minimal CSS edits -
buddhahouse dot org (forward slash) index dot php(forward slash) Discussion-Forum/ (- remove spaces etc)

(- err ... YIKES! you cannot post links in this forum untill you have posted 10 messages - thats fair enough, but if I had not copied my message to the clipboard, then I would have lost this post forever ... grrr ... though the Quick post option does preserve the text - good)

Anyway, I imagine that this (Joomla solution) is similar to the mentioned WordPress solution, but why go for a cute pen-knife when you have a titanium Swiss Army available? WordPress users are such fanatics! hehe

To sum up - dont worry about looking at different forum packages - use your time to become more skilled at CSS - then such questions will become redundant, the stars will align, and all will be well with the universe.