Scaling images before doing conversion or vice versa?

I wonder which one among methods below should preserve more details of images:

1. Down scaling BGRA images and then converting them to NV12/YV12.
2. Converting BGRA images to NV12/YV12 images and then down scaling them.

Thanks for your recommendation.

Updated 2020-02-04:

For my question is more clear, I want to desribe a little more.

The images is come from a video stream like this:

Video Stream

1. -> decoded to YV12.

2. -> converted to BGRA.

3. -> stamped texts.

4. -> scaling down (or YV12/NV12).

5. -> YV12/NV12 (or scaling down).

6. -> H264 encoder.

7. -> video stream.

   The whole sequence of tasks ranges from 300 to 500ms.
   The issue I have is text stamped over the images after converted
   and scaled looks not so clear. I wonder order at items: 4. then .5 or .5 then.4

Noting that the RGB data is very likely to be non-linear (e.g. in an sRGB format) ideally you need to

1. Convert from the non-linear "R'G'B'" data to linear RGB (Note this needs higher bit precision per channel) (see function spec on wikipedia)
2. Apply your downscaling filter
3. Convert the linear result back to non-linear R'G'B' (ie. sRGB)
4. Convert this to YCbCr/NV12

Ideally you should always do filtering/blending/shading in linear space. To give you an intuitive justification for this, the average of black (0) and white (255) in linear colour space will be ~128 but in sRGB this mid grey is represented as (IIRC) 186. If you thus do your maths in sRGB space, your result will look unnaturally dark/murky.

(If you are in a hurry, you can sometimes get away with just using squaring (and sqrt()) as a kludge/hack to convert from sRGB to linear (and vice versa))

For avoiding two phases of spatial interpolation the following order is recommended:

1. Convert RGBA to YUV444 (YCbCr) without resizing.
2. Resize Y channel to your destination resolution.
3. Resize U (Cb) and V (Cr) channels to half resolution in each axis.
   The result format is YUV420 in the resolution of the output image.
4. Pack the data as NV12 (NV12 is YUV420 in specific data ordering).
   It is possible to do the resize and NV12 packing in a single pass (if efficiency is a concern).

In case you don't do the conversion to YUV444, U and V channels are going to be interpolated twice:

• First interpolation when downscaling RGBA.
• Second interpolation when U and V are downscaled by half when converting to 420 format.

When downscaling the image it's recommended to blur the image before downscaling (sometimes referred as "anti-aliasing" filter).

Remark: since the eye is less sensitive to chromatic resolution, you are probably not going to see any visible difference (unless image has fine resolution graphics like colored text).

Remarks:

• Simon answer is more accurate in terms of color accuracy.
  In most cases you are not going to see the difference.
• The gamma information is lost when converting to NV12.

Update: Regarding "Text stamped over the images after converted and scaled looks not so clear":

In case getting clear text is the main issue, the following stages are suggested:

1. Downscale BGRA.
2. Stamp text (using smaller font).
3. Convert to NV12.

Downsampling an image with stamped text, is going to result unclear text.

A better solution is to stamp a test with smaller font, after downscaling.

Modern fonts uses vectored graphics, and not raster graphics, so stamping text with smaller font gives better result than downscaled image with stamped text.

NV12 format is YUV420, the U and V channels are downscaled by a factor of x2 in each axis, so the text quality will be lower compared to RGB or YUV444 format.
Encoding image with text is also going to damage the text.

For subtitles the solution is attaching the subtitles in a separate stream, and adding the text after decoding the video.