I have stayed at both locations last June.

Overall, I have to say I prefer the HGI in Burlingame. It's located in a more interesting location (you can even see SFO across the bay). Doubletree and Embassy Suites are just across the steets.
It's also newer in comparison to HGI SFO North.
Meanwhile, HGI SFO North is located in a middle of nowhere (surrounded by office buildings).
Both HGIs provide free shuttle to the airport.
However, as a Gold member, if breakfast is really important to you, the one in SFO North will be a better choice as it provides free buffet. The one in Burlingame only gives free continental breakfast.
If you are using your points for the stay, I would rather chip in another 5,000 points for a suite and guaranteed free breakfast buffet! Better value for your points. Just my opinion...

Funny thing is back in June, only HGI SFO North charged me for $2.50 energy surcharge...and it wasn't listed on the website! Considering it is in CA, I didn't argue about it.

Have a pleasant stay there!