In recent years, I’ve found booking directly at the hotel’s website gave me the best prices and choice of rooms, as they didn’t have to give the booking engines a commission. Downside is that the good prices usually come with the conditions of prepaid and non-refundable. FWIW, this has been my experience and I’m sure others have had a different experience.
I also like to deal with the hotel directly if at all possible. I’ve heard of stories, as well as experienced myself, booking engines that won’t come to the customer’s aid when something goes wrong, and the hotel claiming they can’t do anything as the customer booked via a booking engine. And these were big sites, not some fly by night. But I think this doesn’t happen often.
I still use booking engines and travel agents sometimes, if I think it’s more beneficial for that particular circumstance. For example, I booked liveaboards using booking engines, because they offer the sale prices. I can also imagine booking liveaboards directly could be less than efficient due to language barriers, inconvenient payment, timezone difference, etc.