For most riders, the honest answer is no. Dura-Ace delivers Shimano's absolute best—lightest weight, most refined shifting feel, and top-tier aesthetics—but the performance gap over Ultegra is surprisingly small. You're paying a significant premium for marginal weight savings and slightly crisper shifts that most non-professional riders won't notice during regular riding.
Where Dura-Ace makes sense is for competitive racers chasing every possible advantage, riders building no-compromise dream bikes, or anyone who simply wants the best available. The current generation is electronic (Di2) only, so you're getting flawless wireless shifting—but so does Ultegra Di2 at a much lower price.
Think of it this way: Ultegra gives you roughly 95% of Dura-Ace's performance at a fraction of the cost. Unless you're competing at a level where grams matter or you have the budget for a flagship build without compromise, Ultegra is the smarter choice for most serious road cyclists.