Hi, I'm lumia 620 user, I've been using BL-5J for about one year, the new BL-5J is about 1430, so it give more up to 10% capacity.
There is a piece of plastic/rubber thing inside the battery cover, you need to trim it completely in order to fit the battery inside.
And about battery capacity, it's not an absolute measurement, it may be slightly higher or lower , and over the time it's capacity would drop. That mean if you use your old battery it could be around 75-85% rate of label.
Also don't believe conventional "double-power battery", battery is just like a gallon of gasoline, in order to make a double capacity battery you need more cell of battery, like more volume of gasoline. The reason of nokia's new battery is slightly higher is because they use thinner electronic circuits to give more space to battery cell to fit in.