Sony replacement battery - lower than original capacity

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I have a Sony VGN-SZ4XWN/C laptop which is fitted with a VGP-BPS2C
battery, which is marked at 11.1V/5200mAh. Yet when I look for a
replacement on the Sony web site, I find there are two available - one
high capacity one, which is larger than the original and also the
replacement, but which is of lower capacity.

VGPBPL2C.CE7 - 7200 mAh at   279.00 inc. VAT
(I assume that is larger, and so does not fit as well).

also VGPBPS2C.CE7 at 139.00 inc. VAT
which is described as "Replacement Battery for VAIO S/SZ, FE, FS, FJ,
C and AR Series" One of the specs is Power: 53.28Wh (11.1V/4800mAh)

Any thoughts?

Any thoughts about where I might get a decent 3rd party spare? My
original is still OK, so I can't use one of the places that uses the
original case, but puts in new cells.

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