What are the experienced VNA users think when it comes to 6 GHz VNAs?
Better buy an old HP 8753 or a PicoVNA for HAM usage?
I think those are both decent choices and you can decide based on price. Haven't used or seen a PicoVNA, but the specs look good, although it has a price to match.
There are many 8753's out there and spare parts and knowledge are easy enough to find. The main issue with the 6GHz A/B/C models is that the test sets are hard to find and expensive. Expect to pay over $1000 for a 6GHz test set and between $500 and $1K for the 8753 itself depending on condition. Then you will need a cal kit and adapters for the APC-7 connectors.
Personally I don't have a test set, instead I use a dual directional coupler from an 8752 from eBay. I built an RF doubler which I use for the 6GHz range.