Is mobile data more reliable than the Wi-Fi at my resort (e.g., in Tucker's Town)?

Yes, for mobility and price. Most luxury resorts on the island charge very high fees for "premium" Wi-Fi, and it often only works in the lobby or room. A personal eSIM gives you a private, fast 4G/LTE connection that works everywhere, by the pool, on the pink sand at Horseshoe Bay, and, most importantly, when you leave the resort to explore.