In Hong Kong, of course, since you will look for foreign brands and when those enter China they are taxed heavily, and not in Hong Kong.

But be well aware of the possibility of being shown fakes, or counterfits that look just like the original.  If a deal seems too sweet, be aware of the fake possibility.

I would say Hong Kong too. I've been to both places. Either way it's not cheaper than where I'm from so I usually don't shop in either place. I will occasionally get something, but not a lot. So by your standards cheaper would be in Hong Kong. Although you can find cheaper in other places in the world. But still Hong Kong has really cool markets and it's a better place to shop as far as being fun to me. A lot of tourists there! Check out some of the markets on the street and the famous ones near the Bay over by the Hong Kong starwalk. 

depends what you are going for, if you want genuine brands and a nice wester nshopping experience then HK is great, there is very little else to do there but shop. I cant comment on Beijing as I havent been there yet.
If you just want to buy stuff and not too bothered if it is fake or out the back of the factory or indeed chinese brand (maybe with some obsurd english sentence on it) then go to shenzhen. Or maybe further inland to Humen or Houjie in Dongguan City. This is where a shed load of clothes and shoe factories are located and alot of it finds its way into local shops and markets.

both  bj and hk are not that cheap when it comes to taobao

Yes, foreign brand clothing is much cheaper in Hong Kong.
You should go to Causeway Bay.  The malls are nice, but you will find better deals walking the streets.
Also next door to Causeway Bay is Wan Chai, and there you can find many small shops selling factory direct for cheap.
Have fun, I'll be there this weekend too.

There's no comparison really.

Hong Kong has most of the lines you might expect to find in London or New York.
Hong Kong has malls all located close to each other.
Hong Kong has boutiques dedicated to western labels/designers.
Hong Kong prices are about the same or cheaper than you might pay in the UK.

Beijing you always have the transport issue (metro's 2miles apart).
Beijing shopping involves an investment in transport and research into malls stores and locations.
Beijing shoe sizes and jeans are to fit the Chinese shopper, you may find limited supply in your sizes.
Beijing shop assistants will expect you to communicate in Madarin.

https://www.scmp.com/lifestyle/food-drink/article/2159199/where-family-man-hong-kong-goes-eat-good-value-high-quality

Obviously the price in hongkong will be more acceptable (foreign brands)

you better try Guanzhou!! you will shop with a huge plastic bag till you drop its like a give away price for very nice clothers, shoes and bags!!! ofcourse at the wholesale market!