No. That is not the average pension under each system. It is the maximum full pension someone would get if they had paid (or been credited) with the number of years required to get a full pension.
The old system IS a two-tier system - basic pension and additional state pension. The new system is a single-tier system.
You need to try to think about this differently. Someone under the old system could have a two-tier pension of almost £400 pw, £176.45 plus £221.10 additional state pension through paying into SERPS/SSP. Why do you think that is? Why are they getting so much more than you are and are you complaining about it?
www.gov.uk/government/publications/benefit-and-pension-rates-2025-to-2026/benefit-and-pension-rates-2025-to-2026#state-pension
If you only receive £169 compared to the full basic rate of £176.45 then there will be a reason for that shortfall. Either you are short on contribution years, didn’t pay SERPS or were contracted out of SERPS (and so have a private pension) or paid married woman’s stamp for some years.
If someone has an income of only £169 they could claim Pension Credit to bring their income up to £227.10 pw (at current rates). This would be just £3.15 pw less than someone receiving full new State Pension*. However, unlike them they would have been able to claim (last year) Winter Fuel Payment of £200 or £300 depending on age, Warm Home Discount of £150 plus help with dental and eye care and a free TV licence if over 75 - making them better off than the person receiving new State Pension.
* The rate of Pension Credit is deliberately kept just below the full rate of the new State Pension so that those receiving the latter that are prevented from claiming those other benefits
Now that WFP has been reinstated (for people with an income up to £35,000), the person receiving Pension Credit will still get the Warm Home Discount and the other benefits.
For someone reaching SP age after 5 April 2016, but with NIC paid before and after that date, DWP do two calculations to see if they would have been better off under the old or new systems. If some would have been better off under the old system, because they paid into SERPS, they have a protected payment.
Ask yourself this. If everybody reaching SP age after 5 April 2016 was better off under the new system there would be no need to do the two calculations, would there?
Someone whose entire working life is after 5 April 2016 will never be able to build an additional state pension. It is a single-tier pension. It was introduced to save the government money as paying the State Pension becomes more and more unsustainable.
And, as I explained above, older pensioners have much better spousal inheritance rights than younger pensioners. Depending on age, someone on the old system might be able to inherit their late spouse’s basic pension to top up their own to £176.45 a week (at current rates) and 100% of their SERPS. People reaching SP age after 5 April 2016 cannot inherit any of their late spouse’s basic pension and only 50% of their SERPS. Those who were under 55 when they were widowed get far less than that, even nothing.