Is it a class C, or a /24?
Regardless, longest match wins. If old provider is announcing your space as part of a larger announcement, you'll be a bad netizen for a few days because you're violating the RFCs concerning inconsistent AS, but your traffic will swing almost entirely over to new provider, and rather quickly. Traffic originating in old provider's network will likely still come in on your old link. (I've done this for three new customers in the past month.) If your old provider is specifically announcing your space as a /24, standard BGP path selection processes will take place all over the 'Net, and YMMV on the traffic balance. On or before disconnecting the link to old provider (if they are specifically announcing your /24), be sure to have them stop announcing that /24.
Senior Staff Engineer