The same accelerated export you have in AME and Premiere Pro is now available for H.264 export in AE.
H.264 export also supports both Hardware and Software Encoding modes. Not every option that is available in AME is exposed inside AE, and some settings such as resolution, frame rate, color management, are still set from AE’s Render Settings or Output Module Settings, but there should be enough to tweak for most users. If you need more control, you can customize the H.264 settings by clicking on a Format Options button in the Output Module Settings dialog. We have also included 3 H.264 presets to get you started. This integration utilizes the Adobe Media Encoder (AME) UI along with AME’s backend encoding system all without leaving After Effects. Starting with Beta build, AE 23.0x11, H.264 is now available as an option in the Output Module Settings dialog allowing you to encode to H.264 directly from the AE Render Queue.