Fair question, because both terms get used loosely on product pages.
Here is the real difference. Standard sticks, often called ALPS-style or potentiometer sticks, read position through a wiper sliding on a carbon track. That contact is what wears and causes classic drift. Hall effect sticks put a magnet on the stick and measure its field with a sensor that never touches it. TMR, short for tunnel magnetoresistance, uses the same magnet idea with a different sensing element that changes resistance with the field instead of producing a voltage.
In practice TMR has two concrete advantages. It draws much less power: GuliKit quotes roughly 0.1 to 0.3 mA for a TMR sensor against roughly 0.5 to 2 mA for a linear Hall sensor. That matters for battery life in wireless pads and is why TMR modules can drop into controllers designed for potentiometer sticks without circuit changes. Many players also find TMR pads feel tighter around centre than early Hall effect pads.
What I would not believe is that TMR has dramatically higher resolution. Even GuliKit says resolution depends mainly on how precisely the controller's own chip samples the sensor, not on the sensor type. The things that actually decide how your aim feels are the firmware deadzone, the response curve and the spring tension.
For a shooter player who likes the DualSense feel, I would lean TMR, but buy from a retailer with an easy return and test the deadzone in the first week. A magnetic stick with a fat firmware deadzone will feel worse than your DualSense, whatever the box says.
