Where should I go?

My previous and next stops would matter.

I haven't been to either but would be glad to see both of them. Orkney has some very important early historic sites, which would probably tip the balance for many folks.

Would you rent a car?

Yes - assuming it wouldn't take too long to get there!

We spent three days each in both Lewis and Orkney this June. They are both amazing, but for different reasons.

1) Lewis has the Callanais Stones, the Blackhouses, and St. Clements (look at the carved stones!) but most of Lewis is about seeing the countryside, beaches and migratory birds (in June, at least). Stornoway was in the peak of a Covid outbreak, so things might have been a little off the usual.
2) Orkney has the widespread Neolithic artifacts and old castle ruins and WW2 things. Also a lot busier.

As long as you're probably getting on a plane to puddle-jump (using the ferry is a big time investment, especially for a three day visit), you might want to consider Shetland, where we also spent three days - that's the one we'd head back to first. Orkney would be next.

Our opinions are sometimes overly influenced by seeing mobs of puffins. Our second influencer is good trad music, and we only found that on one of nine nights (in Lerwick). That ratio might improve in peak season.