The first one is a read-only field, while the second one gets compiled as a pair of methods (and all reads of the property ProductLocation gets compiled into calls to the corresponding get method and writes to it gets compiled into calls to the set method; internally, these methods will read from / write to an internal, automatically generated, non-read-only field). I’d say the most important difference is thread-safety! (how? read on!)
The basic usage of the class will look exactly the same: code in other classes will only be able to read the value, not change it. Also, the code to read the value will look exactly the same (for example, print(myInstace.ProductLocation); here, you cannot tell how it has been declared, cool, eh?)
The first, most trivial difference is that the property with private setter allows for instances of the same class to modify the value, while in the case of the readonly property, not even the object itself will be able to change the value.
Now, for the thread-safety. The readonly attribute on the field will change its memory visibility semantics when you are working with multiple threads (just like Java’s final fields).
A readonly field can only be assigned to at declaration or in the constructor. The value assigned to a readonly field cannot be changed (at least not in a normal way) and it is guaranteed that every thread will see the correctly, initialized value after the constructor returns. Therefore, a readonly field is inherently thread-safe.
To achieve the same thread-safety with the property, you’d have to add some synchronization on your code, which is error-prone. It might lead to dead-locks, data races or reduced performance, depending on the case, and especially if you are not experienced.
So, if the value represents something that semantically cannot be changed after the object’s construction, you should not declare a private setter (this would imply that the object might change it). Go for the readonly field (and maybe declare it private and declare a public property with only a getter accessing the field! This is actually the preferred form, since it is not good to expose fields, it is better to only expose methods — there are many reasons explaining why in this answer)