It isn't always. Covers of songs by Glee are proof that the original isn't always better. If the original was always better, there would be no development and the world would be very different. 

When original is better it is often down to familiarity, and the associated feeling of comfort. 

Maybe most people who can do something better prefer to do something of their own?

As some people have helpfully pointed out, it ain't necessarily so. However there are some principles that do contribute to the effect, which is perfectly genuine. One is that many a mediocrity who manages to achieve a position of sufficient authority to command the necessary resources reckons that he can do something that someone else has done before, and do it better, now that the other person has taken care of the problem of achieving originality.

Mediocrities in such a mode practically invariably deluded themselves.

Another factor that trips up even many non-mediocrities (though usually non-mediocrities have too much sense and too many demands on their talents to make fools of themselves in such a way) is the fact that the first version of any great success usually is based on something that the creator understands at an intimate level. Imitators often lack that contact and the intimate insight, and they produce what amounts to a lossy translation. It is like many American imitations of European movies. Usually the effect is tooth-grating in the extreme and other places.

Then there is Fred Brooks' Second-System effect. You have seen something done once, so now do it again, but this time adding in all the bits that you didn't have time or resources to put in on the first attempt. Read his book: "The Mythical Man Month".

Similarly relevant is the principle of "Systemantics" expounded in the book by that name, written by John Gall. If you haven't read it, run, don't walk, to the nearest library or bookshop.

Of course, such principles apply equally strongly in producing almost anything relevant to that question, not just software systems and large-scale engineering.

Also, concerning the arts, once we are familiar with an old favourite, its character becomes part of what we enjoy about it. Change the character, and it takes something really great to beat what we have learned to expect. On the other hand, a direct crib has little point, so the dice are loaded against the successor, or the "Son-Of-The-Three-Stooges". To be just as good, it is not enough to be just as good.