Dadgum. Well. Damn. Did he do that on the Henry? Hope not.
It's gonna be a decision you gotta make. Which one in your mind has the most sentimental value? If it's the Browning then pick it and don't worry about the resale value being messed up because of the engraving.
If not then pick the Henry?

If I inherited a gun from a loved one, there's no way I would sell it unless I was destitute. That is just me and I completely understand if somebody else doesn't attach sentimental value to material things. I actually respect that too. But if I was gonna keep it for sentimental reasons, I would actually cherish it a little more because of the engraved receiver.

That is good thinking. I have an old tool that my dad engraved his name on. He did it because he and his brother were always working together on stuff and they had the same tools and they would always argue about who owned what tool. So dad engraved his name on some.
I still use it. When I pick it up I always see his name and chuckle. I think of his hands holding the engraver and doing it. I can almost see it and him.
So as you say perhaps OP could look at the engraving and think about his dad's hands doing it. I know I would.

I think you have made a wise choice sir. Knowing the circumstances I would do that as well.
May you have fond memories of your dad every time you handle it or look at it. Peace.