First of all, I think that it is not that difficult to tell the parties apart in the US today. However, that's beside the point.
In theory, strengthening political parties could make the parties more distinguishable from one another. If parties had more power, they could be more vigorous in ensuring that their members adhere to the party's positions. This would ensure, for example, that all Republicans be absolutely opposed to tax increases in order to be allowed to run as Republicans. As things stand today, a party does not have the power to prevent someone from running (and perhaps winning) as a member of that party and thereby diluting the party's message. Strengthening the parties would prevent this dilution.