Depends what your looking for.

Lagos is more of a large town, it is bigger than Alvor with more hotels, apartments, shops, bars and a lovely new marina. It is also further away from other resorts if you like to travel around.

Alvor is more of a small fishing village, with shops, bars and resturants. Alvor also has one of the nicest beaches I've seen, it goes on for miles. It is also close to Portimao and P. de Roche if you want more shops and nightlife.

Both are nice. I personally prefer Alvor as I like it quiet.

Hope this helps

would you recommend going mid May or will the weather be not too good, much rain

Weather should be lovely in May.
We have been in November and its been like an English Summer.