I mean that in common vernacular, when someone says "pension", they are referring to a defined benefit pension. Otherwise, in the US, we use 401k, IRA, "retirement funds", or other words.
I'm not sure what you're claiming. It's possible to design a very lucrative and costly defined benefit pension, but in the US, no employer is offering it other than governments, and even the governments are beginning to croak under the stress of unsustainable benefits, so new employees are not eligible for them.
Based on some quick Googling, I don't see what is so much better about an SIPP or a group personal pension plan? SIPP offers some kind of matching from the government, but it doesn't seem significant.
Main one is Tax relief at your highest rate on income tax you get an extra 20% into your pension - if your a higher rate tax payer you can reclaim the extra tax relief.
For a higher rate taxpayer you put in £60 and get £100 in your pension.
You can also do salary sacrifice and reduce you income tax and NI lability
I don't know anything about the 401k system, but the money going into my pension is from my gross salary. Combined with high taxation, it means that it's worth up to twice as much going into my pension as it would be going into my bank account.