Well, first I think it's unproductive to analyze hate-crimes legislation in the context of murder, since penalties for murder are already rightly very harsh, regardless of whether group "hate" was a factor. Instead, I find it most productive to consider hate crimes legislation in the context of lesser crimes where it might, in some cases, make sense to have light punishments, and in other contexts might make sense to have harsh punishments.
An example I've provided before would involve trespassing and minor destruction of property.
Case A: Your neighbor is pissed off at you because your kids keep throwing their balls in his yard and leaving them, your dog keeps taking a dump in his yard, and your big tree keeps dropping leaves all over his treeless lot, which he has to spend hours raking. So, one night, after repeatedly letting you know how upset he is about your family's behavior, he gathers up the toys and the dog poop, and the leaves, makes a big pile in your front yard, and lights it on fire, to send you a message. Nobody's hurt and the only physical damage is a little burnt spot in your grass.
Case B: Your neighor is pissed off at your because you're black, and he doesn't think black folks have any business moving into a white neighborhood, bringing crime with them and driving down property values. So, one night, after repeatedly letting you know how upset he is about your family's arrival, he builds a cross in your front yard, and lights it on fire, to send you a message. Nobody's hurt and the only physical damage is a little burnt spot in your grass.
The crimes, in each case, are physically very similar. He trespassed on your land, destroyed some of your lawn, and was probably guilty of some unlicensed burning or maybe even minor arson. But would you really argue that the two crimes should be punished equally? I would think that the guy in Case A was out of line, but a slap on the wrist would be plenty. The message he sent was sent narrowly to you, and didn't signal much of a threat of violence. By comparison, the guy in Case B needs a lot more than a slap on the wrist. The message he sent was sent to all black people living in or considering moving to the neighborhood, and the symbol he chose was heavy with the threat of violence -- it was a symbol with a well-known history of being a pre-lynching warning.
So, should the differing motivations between Case A and Case B really be treated as irrelevant? Or, given the much stronger reason society has to discourage the kind of behavior in Case B, should the group-hatred behind Case B be taken into account and justify a harsher punitive disincentive for such behavior?
When we start to look at lesser crimes, like that, rather than at murder, it's easier to understand why society would want extra punitive powers to discourage certain behavior than other, facially-similar behavior. Another example might be the difference between a kid who beats up a classmate for personal reasons versus a kid who beats up a classmate for being a Jew. Although it probably doesn't make a huge difference to the immediate victim of the crime whether he was targeted for personal or group-identity reasons, it will make a difference to others. If he was targeted for being a Jew, the attack constitutes a threat against all the Jews in the school, meaning there are more indirect victims. And from society's perspective, there's a greater threat of the criminality developing dangerous social momentum when it's group-based criminality than if it's based in personal differences between two individuals. We saw in Nazi Germany what can happen if violent anti-semitism is allowed to build up momentum within a society. So, one could argue that justifies society doing more to block criminality that is motivated by group animosities than criminality that doesn't include those wider social implications.
The other thing to think about, with hate crimes legislation, is the fact it's used as a way to get federal jurisdiction where a locality might be expected to overlook a crime due to institutional bigotry. If Case B happened to you, and the local police and prosecutors were good old buddies of your cross-burner, who shared his thoughts about black people moving into the neighborhood, you might like the idea that you could appeal to the federal government for a prosecution, rather than relying on the local boys.