Cook shelled peas in large saucepan of boiling salted water until almost tender, about 1 1/2 minutes. Add sugar snap peas to same pan and continue boiling 30 seconds. Drain; rinse under cold water and drain again. Transfer to large bowl.
Whisk vinegar, soy sauce, sesame oil, sugar, salt, and pepper in small bowl to blend. (Peas and dressing can be prepared 2 hours ahead. Let stand separately at room temperature.) Pour dressing over peas in large bowl; toss to coat. Season salad to taste with more salt and pepper, if desired. Serve at room temperature.
