15% or more, depending on how many icons you want to be drawn next to your hotel name. So, with most small and medium hotels that don't have a detached hired team of managers, you can find a direct e-mail, wink-wink, nudge-nudge, and get a manual booking with 5-7-10% discount. Of course, all booking services prohibit such unequal discounts in their agreements, but it is unenforceable, as the hotel can invent any complex reward system for anyone at any time. Booking services know pretty well that their profits depend on eyeball domination, that's why they buy all the ads everywhere, and flood the web with “official” hotel pages in numerous catalogues. Hotel website is pretty much always lost below those. Of course, big hotel networks with their own marketing departments and unique partnership agreements with public and corporate services work differently, and the price you get is what they already want from you.
What is trivially detectable, though, is cancelled bookings that result in immediate unavailability of the same room for the same period. If you book through a service first, then try to get a discount from a hotel, there is a much higher chance that you get “Naaah”. No one would really bother about a single case, but your case might not be that single case.
As for “booking guarantees” given by a “big, well-known service”, read the fine print in the user agreement. It the hotel that is responsible for everything. A decent hotel treats all visitors equally, and tries to double-check for possible problems in advance. A shady place that only needs to get by for a season or two, inflates scores by squeezing positive reviews, and overbooks isn't really afraid of losing a contract. Moreover, that doesn't happen instantly, because booking services get money from commissions, and want their numbers to increase, not to decrease. Also, Booking.com office for some area is, most likely, 3-5 people handling papers and making calls during work hours, they won't personally swat the place to help any client.
You are correct. Marriott, Hilton, and IHG (and probably others) have price match guarantees, offering 20-25% discount (or a load of reward points) on top off of the cheaper rate that you found. Submitting claims can be a little inconvenient, but it’s worth attempting before booking an expensive trip.
Booking through a third party also usually prevents you from receiving loyalty rewards, if that's something you're concerned about.
Also because making it cheaper through something gets called a marketing/business expansion opportunity and they don't want to take the haircut when they don't have to.
That's not my experience, I think most hotels realise that their website needs to be useable but sure I guess there are probably still shitty hotel websites out there.
If you are looking at luxury hotels, of course they will have a fine website. But people often stay at smaller niche ones, that even if it has a website, it is probably several years out of date and was made with some drag and drop html editor, badly.
Sometimes booking direct is expensive and the hotels most of them have a shitty website.