I've funded a few startups that have applied or incubated through these schemes, my $0.02...
It's not free upfront money to start your business. Whether by grant or subsided costs, payments are made in arrears, you need to expend up front. So if you have no funding, you need to get some or put up yourself. It's also not a lot of money overall and spread over 2 years so there's not a lot of cash if you are looking to pay yourself and others coming from later in life or high paying positions; it much more suits a few locals in their 20s living at home doing a startup where the costs of paying yourself and staff is lower.
The Cyberport scheme opens twice a year for applications, the HKSTP scheme is open year round and you can apply any time. Both require companies, if you don't have a company, then start with the CMF/STEP as noted below.
There is a lot of overlap, but very generically, Cyberport tends to bend towards IT stuff (fintech, apps, services, AI, Big Data) and HKSTP towards hardware (plus the biotech, deep electronics tech, etc). But that's very loose and there's a lot of crossover. If the timing is right, I'd suggest to try Cyberport first (you can't reapply unless there's some change to the plan), then HKSTP if rejected. You cannot have an application pending for HKSTP and then apply at Cyberport. The other way round seems ok (as long as Cyberport eventually rejects).
The HKSTP scheme seems easier to get into, likely due to the opening of 5 dedicated floors in the new 19W building and it needs filling.
You don't need a patent to get in, but a good prototype or some, if tiny, market exposure, testing or live customers helps. Team experience also helps winning. These are equity-free schemes so expect some boring forms to fill in, several rounds of pitching and so on as you are dealing with civil servant types, not business or investment types.
Going through the scheme is fairly straightforward as long as you appear to be making progress and hit (or nearly hit) pre-agreed milestones.
If you have nothing, then better to look at Cyberport's CMF scheme or HKSTP's STEP scheme to fund early concepts. Again not a lot of money if you have to take pay, but a small amount to pay for some prototypes if you are currently in another job.
Once in, then there is a lot of help to get you more taxpayer cash.