Please post the images directly to this thread.
It is all about the settings you have selected in the Export dialog window. Post a screen shot of that window too.
Everything is on default settings. I did try mess with the "Additional External Editor" to match the Adobe Photoshop CC presets but that left me with a very small even worse quality export... So i reset it back to default.
Lightroom Export JPEG
Photoshop Saved JPEG
You mean the banding in the sky? Those look like they are single bit steps in sRGB space. I opened the jpegs in Photoshop and you can see the steps are exactly that. They are probably unavoidable in a 8-bit sRGB jpeg. Sometimes they can be made less obvious by dithering. The screenshots are in the colorspace of your monitor and are rendered directly from a 16-bit representation of your image whether you are in Lightroom or in Photoshop and so that will avoid the banding as you are not doing two successive color space conversions (first to 8-bit sRGB and then to the 8-bit monitor profile) but only one (from 16-bit prophoto to 8-bit monitor profile) which avoids the banding.
In Lightroom you cannot control whether it will dither upon color space conversions but in Photoshop you can. In Color Settings, make sure "Use dither (8-bit/channel images)" is turned on.
In case it helps you, I've found the following blog post by Jeffrey Friedl to be a great write-up on jpeg quality settings in Lr:
You can use a different color space such as adobeRGB or DisplayP3 which might alleviate this or you can add a very tiny amount of noise in Photoshop before changing to sRGB and then to 8 bits. This will hide the steps a bit. The main issue here is quantization limitations translating between color spaces and bit depths.
Also Photoshop is supposed to do this noise thing (dithering is simply adding a bit of noise) already but you have to specifically do the change to sRGB and then to 8 bits before exporting to jpeg.
Here is some more info and some guide on how to fix it: Photoshop Actions to fix the banding of Photoshop's gradients.
This is a very common problem in subtle gradients and a limitation of 8-bit images. At some point Lightroom was going to add dithering on conversion to 8 bits but it looks like that hasn't happened yet. What version of Lightroom are you using?
Thank you all for the responses I'll try them out!
I'm using Adobe Photoshop CC + Lightroom package, I assume it's the latest version..?
Check the info screen. It should be 2015.8
In addition to the suggestions already provided you may want to look at your monitor brightness setting. The image histogram shows an underexposed image with a very limited dynamic range. Raising the Exposure setting inside LR will make the sky gradient much less likely to show banding when output to 8 bit/color.
If your monitor brightness is set significantly higher than the recommended 100-120 cd/m2 the LR adjusted image will appear much darker in print output and on a display that uses a more normal brightness setting. That in fact is what I'm seeing on my100 cd/m2 calibrated monitor (see screen shot below). Just something to consider.