The major differences between the 1030 and the 1050 are the 1030 is waterproof to a greater depth, 33' vs. 10'; the 1030 has a wider zoom range, 3.6x vs. 3.0x; and the 1030 is advertised as "crushproof" to 220 lbs., which the touch screen based 1050 isn't.
Both use a semi-proprietary XD card, but come with an adapter that allows you to use a microSD card instead.