Cut cauliflower into small florets. In large pot of boiling salted water, cook cauliflower until tender-crisp, about 4 minutes. Using slotted spoon, transfer to colander. In same pot of boiling water, cook celery until tender-crisp, about 30 seconds. Add to colander; let drain for 5 minutes.

In food processor, pulse parsley, capers, anchovies, garlic, salt and pepper until finely chopped. Add vinegar and lemon juice; purée. With motor running, slowly drizzle in oil. Scrape into large bowl; add cauliflower and celery and toss to coat. Let cool completely. (Make-ahead: Cover and refrigerate for up to 3 days.) Add tomatoes and toss to coat.