In 2017 2.1 million people visited Iceland. In the same year an estimate of 224,000 people visited the Faroe Islands, so all together the islands get significantly fewer visitors, which would indicate that many fewer tourists will be around even in the summer months.
In June 2016 Iceland had 221,900, where as Faroe had only 22,570. (June was the only month I could find for both sources, apologies) Hope this helps!
Edit: To provide context from someone who has been, I've spoken to my uncle who has lived in Iceland during 2016/17. He said that he wasn't around during those summer months, but Iceland was always pretty busy with tourists & was easy to feel crowded. The Islands were far more calm, but tourist spots such as Puffin watching or old ruins are still busy as that's what people come for (and why he went)