HBO Max is currently capped to 1080p HD but there is some consolation. HBO Max delivers 1080p at twice the bitrate compared to HBO Now - 3x compared to HBO in Europe.
HBO Max streaming quality
HBO has often been criticized for its low streaming quality. While it has technically delivered 1080p HD, the low bitrate (level of compression) has made its shows look far worse than 1080p content on competing streaming services.
It is disappointing to see HBO Max launch without 4K HDR support but at least it delivers significantly higher video bitrate for 1080p. FlatpanelsHD is seeing an average of 7-10 Mb/s bitrate for 1080p (with MPEG4 AVC) while streaming Joker, Wonder Woman, Batman v Superman, and X-Men: Dark Phoenix, with video bitrate peak at around 13-14 Mb/s.
For comparison HBO Now and HBO Go typically hovered around 4-5 Mb/s for 1080p while HBO Europe/Nordic is even lower at around 3.5 Mb/s. In other words, you are getting two to three times as high throughput with HBO Max.
Also read: Streaming: Video/audio quality (bitrate)
HBO Max delivers better HD streaming quality than Netflix and many other providers, surpassing even Apple's 1080p bitrate (but obviously not Apple's 4K HDR bitrate).
We are getting audio in Dolby Digital (AC-3) and 384 Kb/s bitrate.
Here are our measurements from Joker (first picture) and Wonder Woman (screenshot) via the HBO Max app on Apple TV.