As several have said here the answer is, based on limited information “it depends”. For instance take Google and Apple. Google let Apple open up the market for screen phones and then came in at lower price and eventually got more share, however, Apple was the demand engine for the segment and couldn’t afford to drive demand as they lost revenue so the segment stalled. This has been even more pronounced with tablets because Smartphones were partially supported by carrier subsidies. So you can, in a predatory fashion, steal our competitor’s customers with a lower cost similar option but at some point, if successful, you’ll need to pivot to own demand generation and your price point may not allow it.
One other place where this works is in retail. Apple picked the best location for their stores showcasing the mistake Gateway made with a similar retail strategy. Microsoft generally placed next to Apple and that gives them similar traffic but this showcased another weakness with Microsoft products, outside of the Xbox, they didn’t pull people into the stores and the Xbox was too different from the other Microsoft offerings to provide strong sales synergy. So store traffic and sales still suffered. The idea was good the execution less than ideal.
Going where the competitor isn’t is better from the standpoint of building a strong organization, this way the firm learns how to generate demand and isn’t just undercutting the competition. It forces the firm to mature its sales and marketing efforts which I believe is critical to the long term health of the company. But the trade-off is higher risk and cost.
One thing about at least some overlap is it helps you focus not just on what your product does but what the competitor’s product does and eventually you will have to compete for business so a blended strategy of primarily going where the competitor isn’t but contesting some high value clients would likely help build a more balanced organization and force a better product/service.