"is probably being done better than I can do it" .. probably you answered your own question with this. How are you going to take him on based on one feature if he is better? IMHO, Get going on another idea.
I meant more in terms of the quickest prototype I can launch; their mature product's version of this feature will be superior to my first creation. I do believe that over time I can compete and surpass them though.
I might be asking myself these questions...
How important would that feature be? Would having the feature make a lot of difference? With this feature would your product be better? Will that feature alone allow you to sell better? How long would it take your competitor to add the feature? Would having this feature help your competitor to sell better?
If competitor will take time and will help him sell better then one option if you develop the feature is you could sell it to him if you can't compete