I do both types of training throughout the year, I alternate between the two, and I can personally attest that:
Lifting heavy, low reps, and frequently... will drive my 1RM up.
Lifting with great volume or high reps, with less frequency, will increase my ability to do more reps at a heavy weight, but my absolute 1RM will go down if I stay in this type of training for over 3-4 weeks.
I've experienced hypertrophy with both types.
Train for specifics. Neural efficiency and comfort under a heavy weight is king when it comes to having a big one rep max, and I've only gotten that from handling heavy weights at 85+% very frequently. My personal experience at least.