Southport-Wigan is my local line - live right next to it. Units used are 142s, 150s and 156s.
Before the December timetable change 156s were more common than 142s, but since the change I've noticed it to be the complete opposite, especially on the Manchester Airport services. The level of 150s has always been the same for quite some time, although someone who hadn't been down it before commented "there's a lot of 150s down here!"
There isn't any specific rule with regards to what units should operate what services as they seem to arrive at Southport ex-Victoria and depart to the Airport depending on the diagrams, although there was a time when 156s were preferred for the Airport services along with 150s, with 142s being preferred for the Victoria (then Rochdale) runs with 150s filling the gaps. One service that has a tendency to be a cert 142 is the 16.00 Southport-Huddersfield.