On a basic level, fining and filtering are similar - they both take out something from the wine to try and improve another facet. In most cases, it's a matter of removing some kind of solids that may sediment out or are causing the wine to be cloudy. While the advantage of a potentially cleaner looking wine may be offset by the stripping out of potentially valuable flavor components in a wine, I think the end question comes down to why do you want to filter?
If you need to get a carboy emptied quickly because you're out of space and want to make more wine, filtering can help to prevent 'fallout' in the bottle and still get your carboy emptied. But if you have the time, many of these items may settle out on their own with bulk aging and you may avoid taking the positives out of the wine.
Filtering also requires more equipment (pads, pumps, etc.). I personally do not filter my wines asI let gravity work for me over time. While other people here do filter there wines, it would take a blind side-by-side comparison of the same kit with part filtered and part not filtered to experience the true effect, if any, on the wine.
- Jim