The plastic is already killing sealife and will continue to do so as long as the plastic is there.
Filter the sea, maybe some creatures dies, but future generations will not be killed by plastic.
This article http://inhabitat.com/the-fallacy-of-cleaning-the-gyres-of-pl... argues convincingly that filtering is a distraction from reducing the amount of plastic which gets into the gyres which is the only practical way to reduce the amount of plastic.
I think this is a simplification which overlooks the parent point.
It seems reasonable that the gyres have always collected crap and sealife has avoided it. Now that crap is plastic.
But, the gyre already provides the function of avoid-getting-killed-by-plastic, so it's not clear why we should aggressively reduplicate that effort.
The garbage patch may offer benefits to the ecosystem which are not immediately obvious. Whereas, filtering is likely to damage the ecosystem in some ways.
Human record of tending to the ocean has not been very good and we're not good at predicting consequences. I recommend watching documentary film "The End of the Line" http://www.imdb.com/title/tt1176727/ before assuming that filtering is a panacea.