The ARRL renewals page (http://www.arrl.org/renewals) says:
Amateur applications can be filed manually using paper forms or
electronically over the Internet. Amateurs may electronically renew
their FCC-issued licenses "on line" via the FCC web using FCC ULS .
FCC permits on-line renewals at 90 days or less before a license will
expire, and when the license has expired but is still within the
two-year grace period for renewal. Licenses that have been expired for
more than two years are not eligible for renewal or reinstatement. If
you have a Vanity License renewal, remember to have your credit card
accessible to pay the FCC Regulatory Fee.
Amateurs may also renew their licenses within 90 days before the
license expiration date, or within the two-year license grace period
after expiration, by using FCC Form 605 by mail to: FCC, 1270
Fairfield Rd, Gettysburg PA 17325-7245. Vanity Renewals will also need
to submit FCC Payment Form 159 and the required FCC Regulatory Fee,
along with the FCC Form 605. After completing both forms, you can mail
your FCC Form 605, FCC Form 159 and your payment to: FCC, Wireless
Bureau Applications, PO Box 358130, Pittsburgh, PA 15251-5130.
Licenses that have been expired for more than two years are not
eligible for renewal or reinstatement.
For a complete list of FCC filing instructions and filing fees go to
the ARRL page Instructions for License Renewals or Changes.
Basically you can either use ULS online at http://wireless.fcc.gov/uls/index.htm?job=home
Or download form 605 (http://www.fcc.gov/forms#605) and file manually.
From what I can tell, the W5YI site just makes it easier to fill out the forms, and they file it for you. I can not determine any specific advantage to using their site. The only disadvantage I can discern is the additional fee for their service.