The simple answer I can hear some people thinking is just give it to them. It works out well enough for the most part, and if the person playing is primarily concerned with mechanics than their value of the item will be directly proportional to how useful of an item it is to them. I am hoping though, especially if you frequent this blog, that you and your players take more then just mechanics into consideration when it comes to value. So, if you want the person to really really like that item, how do you give it to them?
There are two ways to go about this, the first is to simply give it narrative value of some sort. Make it significant to the character for some other reason than just its mechanical benefits. The other is to make them earn it.
We all know an item like this, we probably have one. Something that we own, that we keep, it's not particularly valuable on its own but it has a deep value to us. It is worth a lot more than any monetary value because of the sentiment is holds. A last gift from a dead relative, an inherited item, something from a friend that signifies a special moment. Do what you can to put that into the item you want your PC to value. It's not just a sword that they found, it is the last sword that their father ever made, not the greatest but the last work he completed. It was the sword that their older brother used, and was using when he died. A gift from a close friend, from their first trainer. The possibilities are endless, but if you can impress the value of the relation on the player, and then give them the item they will value it more than if you just give it to them. After all, which would you rather have? A +4 Longsword, or the +4 Longsword that your dad used to protect the Baron from an Ogre the day he died?
Make them Earn It
This also imparts a sentimental value to the character, only instead of doing it via the item's history, it does it by making the weapon a trophy, a monument to a deed they accomplished, a hard fought victory that they earned. I've seen players hold onto items long beyond the mechanical use of it simply because they "liked" the item, as it was to them to proof of the character's biggest victory. Make something hard to earn, or come after a particularly tough moment and it becomes a token of that memory, a souvenir of that time and victory. If you make them earn it, its value inherits the 'value' the encounter had, and becomes something more. This is especially true in larger games where it is a symbol of something they did, that others were not a part of. Something to mark them out as special or individual. It can be a powerful tool.
The point I am trying to make with this is that if you want to give an item to a PC, and you want them to value it, you need to give it a value beyond mechanics. If one GM is giving out items of power, and the other GM is giving out items of emotional significance, is it really any surprise when the "good" players prefer the items of emotional value? If someone just gives you something, it holds no real value. If you earn something from someone, it is special beyond what it does.
So keep that in mind next time you are planning to item drop. If you want them to care, make them care, give them reason to. I've seen players ditch magical and other mechanically better weapon after weapon and keep using their plain old starting sword because story wise it was important to them and would be all they needed. It is an awesome thing to see, especially as a GM because when a player does that, when you get them caring that much about an item, you have new ways to push them, to provoke them. How long will they cling to that item? What if they have to change? What if you take it? Find out why don't you? ;)