Depends on your measurement. In the 60s and 70s real wage rises for most were at around 4-6% so people were better off year on year. Since the 2000s real wage rises have been at about 1.5-1.7%, so people aren't getting more better off than they were in the 1970s. Since the 2000s real wage rises for the very rich have been significantly higher, so if you want to measure living standards by the success of the top 10%, yeah living standards are better. If you want to measure on for instance, house affordability, rent, general cost of living, I think it's extraordinarily inaccurate to say living standards are better today.
Yes, people can buy more 'stuff', but the fact that vast swathes of people are 3 missed pay slips from absolute disaster is not a ringing endorsement of standard of living.