Resurfacing or a new pool deck
Resurfacing is the cheaper way to fix a worn top and freshen the look, but only when the slab underneath is still solid. A coating can't fix a deck that's sunk, heaved or cracked clean through, because the new top just follows the old problem. So I start with the old deck, check for movement and loose spots, and tell you which way I'd go. If it's borderline, I'll say so and lay out both.
What sets the price of a pool deck
Size is the big one, and curves around the pool take more forming than straight runs. Tearing out and hauling off old concrete adds work, so does a backyard that's hard to reach, and a decorative finish or color costs more than a plain broom finish, the light texture that gives your feet some grip. If you need to trim, cut the fancy finish before the base, because nobody sees the base on day one but it decides whether the deck stays put.