You have two issues to sort out here....

1) You were the only game in town until the competitor came along, and guess what, the prices got lower. This is normal and natural in the evolution of companies and their competing products. Eventually, at least once competitor decides to make an issue of pricing. Indeed you have a choice to make. I often advise my clients this way: If you have a great product, and it's priced higher than your competition, you must provide your marketplace with a way to view your product as worth the price. If you cannot to this, then by default, you must lower your prices and by doing so, give up much of your profit.

2) Your competitor's pricing has crept up to meet yours. Without any real indicators blaring to me the truth, I'm betting (from experience) your competitor temporarily lowered their price to gain market share (successfully) but did it at such a low price, they cannot make a profit on the customers they gained. This means you should keep your higher pricing and repeatedly broadcast to your marketplace that you have a superior product at a higher price. Doing this successfully means your competitor will be doing business in an unprofitable zone and will not be able to sustain this for long...and will either come up to meet your pricing or suffer from damaging lack of profitability and cash flow.

I suggest you take the strategy of forcing your competitor to either suffer or meet your price. Please do not lower your price, or lose profit, unless you are unable to publicly justify your product as superior!

Good Luck and get cracking on justifying to your marketplace that your product is superior and worth the additional price!