As usual, the answer is "that depends".
If you are printing a small number of photos, you're probably better
off paying to have someone else print them and mail them to you - the
cost of a printer pays for a lot of postage! However, if you are
printing many photos, the cost per page will be lower if you print
them yourself rather than pay printing and postage, so at some point
your savings per print will exceed the up-front cost of the printer.
However, on a strict costs comparison here, you will almost always
lose doing it yourself, because your investment in a printer won't pay
off for quite a while, and you could be earning interest on the
purchase price had you not bought the printer, making it even more
expensive for you. Your biggest gain in printing yourself is the
control you have over the print process and immediacy in receiving
prints - a few minutes versus days.
In terms of cash outlay, you are probably better off letting someone
else print your photos for you. However, by purchasing a printer you
buy more than the ability to print photos (time saved, control, etc.)
which may make this option a better deal for you personally - this is
something only you can answer.
If this is not the type of answer you are looking for, please request
a clarification and explain what you want.