Cut prices to compete with undercutting competition or not?

My company essentially invented a certain product category many years ago and for about 3 years we were the only company offering this digital product. Because we were the first and only, the we grew fast and quickly this product became our number one seller. It essentially funded us as we were bootstrapped. About 3 years into it a larger competitor came into the market and undercut us by offering the same product at around 50% to 90% less than we were offering it. The product is digital, so pricing is rather arbitrary, but the prices we were originally selling it for were very reasonable and most would agree that the competitor's pricing, while cheap, greatly devalues the product itself. (A common theme with this particular company.) Every since then, we have been hit hard and have lost a huge amount of market share to this competitor. From the vendors that sell this product through my company I hear 2 sides: 1. We should not lower our prices to be like them. Instead we should raise quality and keep the prices the same. (While this sounds ok, the idea of raising quality isn't really applicable in this situation. While we have some control over it, we don't have that much control.) 2. Other say we need to lower prices to compete. In fact, there are some vendors that sell the same product through our company at a higher price and sell the same product through the other company at the much lower price. With our company, we allow the vendors to set their own prices, but the other company does not. They force all vendors to follow their lower pricing points. In the last year or so, the other company has actually crept up its pricing to be closer to ours. So, wondering... should we drop our prices to match or beat theirs? Or, should we keep them the same? Thoughts?