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Analogue sticks are the part that dies first. Conventional sticks use a potentiometer, a physical wiper dragging across a resistive track, and that track wears until the pad reports movement that your thumb never made. Hall Effect and TMR sticks read a magnet with nothing touching it, so the failure mode simply is not there. It is the single specification most worth paying for if you keep a pad for years.
Connection type is the next real decision. A cable removes every wireless variable and is still the reference for fighting games and frame-tight shooters. A dedicated 2.4GHz receiver comes close and keeps the desk clear. Bluetooth is the most convenient and the least consistent, and on Xbox consoles it is not an option at all because the hardware speaks Xbox Wireless instead.