Hi Firstshot,
I have owned both,and currently own the remington LSS in the 3006 caliber.It is beautiful,I have quite a bit of gun smithing work in it.Jewell trigger,floated and glass bedded,crowned.By far the most expensive firearm I have.It shoots great off the bench but I find it to be a little flighty on the off hand point.It serves as my backup gun to a Browning Stainless Stalker in .270.I have owned the LSS for two years and havn't hunted with it.The Browning is like the trusted old friend.I have so much confidence in it I have no reason to use any thing else.
The Winchester feather weight I owned was in the .300 win mag caliber.Nothing at all wrong with it other than it was not at all comfortable to practice with.I miss it but I sold it to a friend who I travel to hunt with every year so I get some visitation rights.
So after all that buy the one you are most comfortable with and get to know it well.With either of those choices you can't go much wrong!