My daughter studies physics at Lancaster and I live in Nottinghamshire and know Nottingham trent, the tram goes through there every time I want to go into the city. Comparitively Nottingham is bigger than Lancaster. But both citites will have all you need when it comes down to little cafes, greggs, primark, jd sports that kinda of thing. Nottinghams nightlife there are more clubs, but Lancaster still has 3, and also has copious amount of bars too.
Nottingham trent uni is split over two campus. City and Clifton campus. Psychology will be on city campus, and you will know your in the city. The tram runs through city campus, then the next stop is 'royal centre' where the theatre royal, cornerhouse (worth googling) and royal concert hall is and closest access to victoria centre shopping center. Following tram stop is 'old market square' and this is where more shops are, the old square and the council building and access to the pavement cafes are in an area called 'hockley'. next stop after that is a lace market which is the top of hockley region and also access the art exhibition centre and caves. Prior to the stop at trent uni, theres an area called the forest and a lot of students tend to live there, as well as city centre.
So if your comparing Lancaster to Nottingham trent, Nottingham is definitely a city uni for sure.
At Lancaster a lot of students including my daughter lived in the city in second year and third year. Some can live back on campus, but a lot lke to live in the city as its close to the bars, cafes etc and short walks to sainsburys, iceland and aldi and poundland. for 4th years shes at chancellors wharf which is uni owned accommodation in the city.
If your courses are like for like and uni facilities like for like, then think about where you are going to live. If you feel a big city uni might be a bit overwhelming living in then go for Lancaster, and vice versa if you thrive in a big city location.