Motives give you something that alignment doesn't, namely some sort of guidance toward a personality. But on the whole, I think when the novelty wears off, the same group of people who dislike alignment would come to loath a motivation system as well.
When people complain about alignment, four things that usually come up are:
1) It constrains and confines the player inhibiting 'role play'.
2) It forces you to accept a label.
3) It leads to metagame arguments.
4) It's too vague to be of any use and so wastes space.
If we replaced alignment with a motive system, I think very quickly the same things would be in play.
Consider a label like 'Justice' as a character motivation. Immediately we are faced with the problem that we can no more get a precise universally agreeable definition for 'Justice' than we could for 'Good' or 'Evil'. Justice is an inherently vague term especially when it comes to application. For some, 'Justice' might mean 'An eye for an eye and a tooth for a tooth.' For others, this definition might be abhorent and the very opposite of how they percieve justice. Instead, they might define justice as 'Recieving a fair trial under the law.' This would force the DM to define what 'Justice' meant in his campaign, which would force players to accept labels that they wouldn't want to accept. A player might consider his behavior to be perfectly 'Just', yet under the DM's definition his character is 'Unjust' - a label he has no desire to wear. Further, if the player was the sort who was inclined to argue over the definition of good or lawful, then the player would be inclined to argue the point whenever the DM's idea of what the just path is differed from his own. This would be especially the case when the motive had some mechanical impact on the game, which, if it didn't, greatly calls into question why you would even bother having labeled motives that don't impact the game meaningfully.
Or consider another attribute like 'Truthfulness'. For some, it is enough to be considered 'Truthful' if you never knowingly say something that is false. That is to say, the important point is your conviction that what you say is true. But we can easily imagine that in the cult of a diety of judgement, destiny, and balance that what is really important is not that you believe what you say to be true, but that what you say actually is true. Thus, we might have side by side, two believers is 'Truth' who would have different behaviors. One is careful not to lie; the other would take great pains to assert only what he could be absolutely certain of and would talk in a very stitled and calculated way when they could even be induced to talk at all. Thus, in this case, if we wanted to describe a cult follower, it is just as necessary to describe the particulars of the cult when we have a motive system as when we have an alignment system.
I don't think we gain a whole lot, and I actually think we lose something. Because, when you design a world to interact with an alignment system, you can be fairly certain that if something interacts with the alignment 'good' or 'evil' or 'law' or 'chaos' that there is a good chance there will be some representative of the alignment around. But if you have a whole list of 30 or 40 virtues or motives, and you have something that interacts only with 'Truthful' ones or 'Humble' ones or 'Valorous' ones or 'Arbitrary' ones or whatever, the chances of the interaction are probably reduced unless everyone is keeping up a fairly long list of motives and virtues.
Worse, if we have people picking from a bunch of motives, the chances of conflict between them increases, which greatly increases the risk of metagame arguements breaking out over interpretation. What if a character takes both 'Just' and 'Merciful', for example? Won't there then be continual argument over whether in some case justice or mercy should win out? Some cases are less obvious than this but no less divisive I think, such as the conflict between 'Honesty' and 'Pride'. Again, virtues are generally no better defined than 'Good', and some level of interpretation will be campaign specific.