Great work, David! Both cards look clean, but I'd lean towards the 'No Border' option.
The 'No Border' card leverages the white space and subtle shadow (assuming there is one, or the background contrast) to separate the element, which feels more modern and less visually noisy.
Yeah I think a ghost button probably help with visual hierarchy like you said. The gradient on the second button definitely detracts a little bit from the main one
It will depends a lot of the rest of the design where they are in, if your design is more software I recommend the border, if not, recommend the without.
Wanted to go with boarder but no boarder got better visibility and I hope you know why! But, I wonder if you try to give no boarder about 1px of solid color boarder then that might work too. Just sharing my options. Good work either way, mate!