Post the x264 log, make sure its of a recording of at least 5 minutes of high action content.
Maybe someone familiar with the AMD encoder can comment on that one.
There's some inconsistencies that I can see in the AMD log though. You say you're playing at 2560x1440, but yet I see in the log that your base resolution is 1920x1080 and your output resolution is 1280x720, but (again) the AMD encoder sees your resolution as 1920x1080. So it seems like you're downscaling twice and upscaling once? Your framerate is set to 30FPS but the AMD encoder sees it as 60fps, is it decimating then duplicating?
18:16:38.568: output 1: pos={0, 0}, size={2560, 1440}, attached=true
18:16:39.453: base resolution: 1920x1080
18:16:39.453: output resolution: 1280x720
18:16:39.453: downscale filter: Bicubic
18:16:39.453: fps: 30/1
18:18:51.653: [AMF] [H264]<Id: 5> Format: NV12 601 Partial
18:18:51.653: [AMF] [H264]<Id: 5> Resolution: 1920x1080
18:18:51.653: [AMF] [H264]<Id: 5> Frame Rate: 60/1
Set your base resolution to your actual resolution. Set the framerate in all places to what you want to record/stream at. Set the output resolution to what you actually want to stream or record at (if recording, I'd recommend just recording at the base resolution, no downscaling, unless your editor can't handle >1080p or something).
18:19:27.838: Output 'Replay Buffer': Total encoded frames: 2171
18:19:27.838: Output 'Replay Buffer': Total drawn frames: 2171
18:19:27.838: Output 'Replay Buffer': Number of lagged frames due to rendering lag/stalls: 543 (25.0%)
Your test was only 30-some seconds long. You want to do a 5 minute (minimum) test under harsh conditions (lots of visual game action) to get valid results. And when well configured it should have less than 1% lagged frames (yours is 25% right now).