I travel both on BA and LX regularly and would strongly recommend LX:

Short haul segment
LX - from MXP you will get a very small breakfast and an fantastic view of the alps
BA - will serve you a so called hot breakfast, which is not edible

Lounge:
LX lounge situation when connecting to the US in ZRH is poor as the general offerings on both the Biz and Sen side
BA lounges in T5 are possible the best "flagship" lounges any carrier offers for BIZ across Europe

Longhaul:
LX - will provide you with a fully flat seat and excellent catering - it's not quantities but very high quality and prior to landing you will get served tasty snacks (Salmon, hash-browns, salad, ...) form the trolley
BA - will most likely not have your preferred choice available and not even the chicken will be tasty. Prior to landing you will be served a foil wrapped sandwich that is below the quality of what you would buy in a gas station shop

US terminals:
LX- has a nice lounge in T4 which unfortunately is prior to TSA. On the other hand, flights tend to leave on time and when you get in there is a gat available
BA - the terminal is OK, food in the lounge tasty and you can enjoy a complimentary treatment a the elemis spa

My verdict: Of the all the carriers I've so far flown north atlantic in C I would rate them as follows: LX>LH>BA>CO>AA>UA

Hope this helps