Neither are particularly wonderful airports, although LIN is a little smaller, so is generally a little easier, as well as being closer to the city. If you're taking a taxi, then LIN will work out cheaper probably. LIN only has bus as public transport, whilst MXP has an express train and bus.

The BA MXP Terrace lounge is now closed, so there is a shared 3rd party lounge (I haven't used this lounge, but the other 3rd party lounges i've used in MXP have been ok). The LIN Galleries Club lounge is not bad, although there are no windows.

I would lean towards LIN, although using MXP is hardly the end of the world. Both are old and shabby.