I'm not sure where you got those figures from, they seem a bit too good to be true. 370 hours is next to impossible for Li-ion batteries (when they are attached to smart phones). 370 hours is more than 15 days. As of 2013 there is no Android powered smart phone that can last in standby for more than 15 days. It doesn't cost a ton of battery to be connected to a cell tower, but over hours and hours of being connected, it adds up to be a lot. Plus add in a ton of background processes to the mix and you have yourself a battery eating machine.
And your figure isn't really practical anyway because I could not think of anyone who could let there phone sit on standby for 15 days without using it.
I know 2 people who have the S4 and both of them said that they can't get more than 2 days out of their charge with practical use.
So to answer your question, there is not a big difference between the two, but the S4 does come with some nice software to help you make the most out of your battery with practical use:
If I had an S4 I would definitely check this out because if you want to get the most out of your battery, this "Smart Screen" is a great start.
from Wonder How To
I think that this is the article you were referencing. This artical states that the "average" battery life is 57 hours:
now 57 hours is a more manageable number. I was interested in how the S3 did in the same test. Here are the results:
Now all of that said, the difference between the two is only 14 hours. 14 hours is a great improvement for Samsung's next S generation phone.
Don't always believe things you see on the net =)