Re: whats the difference
Let me be the first to tell you that if you look around a bit you will find tones of information about this. That said, I will answer your questions in the order you asked them.
Q1, Which shoots better out of the box?
There is really no way to definitively know which rifle will shoot better out of the box. Sometimes you get a clunker and sometimes a nail driver. However, between these two rifles, the Savage is likely to shoot slightly better out of the box. It has a slightly better stock and slightly better trigger. But this does not mean it is the better option.
Q2, Does Remington have an accu-trigger/stock?
No, because they don't need one. Something that you need to realize is that Remington understands that one huge reason people choose their rifles is the unmatched aftermarket. Most of the people that buy the 700 intend on changing it into their own rifle. Mine for instance has a different trigger and stock. If you choose the 700 yours will probably be customized they way you want it. Furthermore, The aftermarket parts that are available for the 700 are superior to the accu-trigger/stock that Savage uses. I personally own a Savage with both accu-accessories and they are not nearly as good as the aftermarket stock/trigger on my 700.
Q3, Do I have to bed the Remington?
Bedding that plastic stock that the 700 comes in is a total waist of time, money, and energy. This is because you will more then likely be replacing it with something much better. The accu-stock Savage, on the other hand, you are stuck with that stock. Because of the positioning of the mag release and action screws it really doesn't work with any of the aftermarket stock available for Savage rifles.
Q4, Do ether of the rifles shoot less than .5moa out of the box?
Not sure why this magic number is so important to you. The answer is probably not. My Remington shoots under a half minute with quality hand loaded ammo and sitting in an AICS. My accu-Savage shoots closer to .75moa with hand loads.
Q5, Which rifle is <span style="font-style: italic">better</span>? (this is the question you actually wanted to ask but didn't come right out and say it)
It depends on your definition of the term <span style="font-style: italic">better</span> If you don't want to do anything to the rifle and just shoot it once in a while then you may be better off with the Savage. However, if you want a rifle that you can change to better fulfill you needs and preferences as you grow and improve as a shooter then the Remington is probably a better fit for you.
My own personal observation:
Judging by the way you asked your questions your probably quite new to this and that's totally fine. One thing you need to understand is that you can't just pick up any old rifle, go out to the range, and shoot amazingly small groups all day long with any old ammo you happen to buy at the store.