Depends what you're using it for. For graphics, no, it won't matter. That GPU isn't fast enough to fill that much memory. Only exception being if the 2GB is GDDR5 and the 1GB is DDR3, then definitely go with the GDDR5 version. If both memory types are the same, get the 1GB...again unless they're the same price, then might as well get the 2GB
Depends what you're using it for. For graphics, no, it won't matter. That GPU isn't fast enough to fill that much memory. Only exception being if the 2GB is GDDR5 and the 1GB is DDR3, then definitely go with the GDDR5 version. If both memory types are the same, get the 1GB...again unless they're the same price, then might as well get the 2GB