Post-AA in games more often than not is FXAA. It's not applied to the edges, like MSAA, etc, but to the whole image. It's very 'cheap' in terms of performance, which is why it's included alongside things like MSAA a lot of the time. The problem is it tends to blur away a lot of details (since it's affecting the whole image, not just the edges). SMAA is also a cheap method (not quite as cheap as FXAA but more or less), but it doesn't blur and soften as much, which is why oftentimes it's far preferable to use that instead. There are some instances where FXAA might be preferable, but they are few and far between and generally are as a result of it being used to correct something else that the in-game processing does terribly.
In general, SMAA is a very good, cheap version of anti-aliasing, and on custom ultra high settings (which might cost you a couple of fps at most - depending on your computer) is more than enough for regular gameplay at 1080p. If you can use something like MSAA via your driver or in-game as well then it'll look good. If you're hotsampling using SRWE (or downsampling via your driver or some other method) that acts as a form of SSAA (supersampling anti-aliasing) - which is what downsampling was originally intended to achieve anyway. So in DA:I, if you're hotsampling for your screenshots, you don't need lots of AA anyway. I just use SMAA, no MSAA. It's down to personal preference of course.
Be aware as well not to overdo it with the lumasharpening. Particularly if you're hotsampling, as when you resize back down it'll automatically look sharper. If you're uploading to flickr as well, flickr uses its own sharpening algorithm for all resized pictures (so everything except the original size that they store). IMO sharpening should be used to gently enhance textures and counter any SMAA/FXAA softness - too much looks bad.
I'm not so much worried about when I hotsample, but just for regular gameplay I notice a huge difference with MSAA disabled, particularly with tree branches. It just tweaks my gourd so I keep it on. I also don't always have the opportunity to hotsample. I do a lot of recording with Shadowplay, which doesn't work if you are running in Windowed mode (which you need for SWRE). So if I'm in a position where I can't switch to Windowed mode, I work with what I have. In those instances, having MSAA active helps.
Would you suggest trying to override the game settings with NVIDIA Inspector? I currently have it set to use the in-game settings. When I tried even the max SSAA setting with it I didn't notice a lick of difference.
What lumasharpening setting do you use? The preset I use has this setting:
/*-----------------------------------------------------------.
/ LumaSharpen settings /
'-----------------------------------------------------------*/
// -- Sharpening --
#define sharp_strength 1.3 // [0.10 to 3.00] Strength of the sharpening
#define sharp_clamp 0.01 // [0.000 to 1.000] Limits maximum amount of sharpening a pixel recieves - Default is 0.035
// -- Advanced sharpening settings --
#define pattern 3 // [1|2|3|4] Choose a sample pattern. 1 = Fast, 2 = Normal, 3 = Wider, 4 = Pyramid shaped.
#define offset_bias 0.5 // [0.0 to 6.0] Offset bias adjusts the radius of the sampling pattern.
//I designed the pattern for offset_bias 1.0, but feel free to experiment.
// -- Debug sharpening settings --
#define show_sharpen 0 // [0 or 1] Visualize the strength of the sharpen (multiplied by 4 to see it better)