Schilthorn or Grindelwald first

Better in what way? Views are terrific from either but since you are in Grindelwald for such a short time why make the trek to the Schilthornbahn? You can ride the magnificent Eiger Express to Eigergletscher or the Männlichen cable way to Männlichen. You can even do a round trip with a hike; Grindelwald to Männlichen; hike to Kleine Scheidegg; Jungfrau train to Eigergletscher ; ride the Eiger Express back to Grindelwald.

First is nice but I think the options above are more interesting. Just my two pennies.

Close your eyes if you decide to ride up to the Schilthorn or First if you are scared of high heights.

Let the weather at the moment decide. The weather up top can be different than below, and can change by the time you get there, Ask your hotel for advice as there are live webcams on the mountains. A sunny day on top is what you want.