Puppy paws or Tri bars?

Where I live I have a long connection of cycling path right outside my doorstep, sometimes going 10km without a single stop light or pedestrian crossing, and thus I have adapted to the puppy paws position on my bike. This got me thinking if I should invest in some tri bars for about $40 (yes, budget but the reviews were good) to make that long non-stop travel easier, or if simply continuing puppy paws should work the same.

On another note, if I were to add tri bars, since my current bike is a road bike with flat bars, would I need to swap it out for drops?