The main thing to make sure of is the battery chemisty is correct (lithium ion in this case) and the voltage, which appears to be the same. Different manufacturers may claim different mAh capacities for their batteries, either justifiably or falsely.
1000mAh (1000 milliamp hours) equals 1 Ah (one amp/hour) which means that when fully charged it will be able to supply 1 amp at the rated output voltage for 1 hour. In actual fact it's not as simple as that, but the exact details don't need to be explored here.
Generally the rating claimed should be the acheivable capacity that can be utilised for the majority of the life of the battery. New batteries may exceed the rated value by as much as 5% or more, but if they fail to perform to the specification then you can consider them faulty in some way.
Some unscrupulous manufacturers from some countries may claim the new battery capacity, not the capacity it will still have halfway through it's warrantied usable life, because they know the average person will have little idea about what it means beyond "more is better" and will have no means to accurately test the claim in any case.
New batteries will need to be cycled two or three times before they will start giving full capacity, though battery manufacturers are doing much better in this regard these days.
You'll probably have noted by now there's really not a lot of difference between 1000mAh and 1050mAh. The claimed difference may be due to the way the manufacturer tests and rates its product, or it may indeed have that tiny bit more capacity due to manufacturing improvements which are being made all the time.
