The CSS11501S has SSL support - the 11501 does not.
The 11503 is modular and the SSL module can be purchased separately.
Session persistancy exist on both platforms.
The advantage for the 11503 is its modularity - so you can add new modules [ie when we release a compression module, you can simply add it in your chassis] and 2nd advantage is the capacity to use every module in the chassis to switch traffic, so if you have 3 modules you get 3 times the performance of the 11501.
Regards,
Gilles.