The center
tag was deprecated not in HTML5 but already been deprecated since HTML4. It simply carries the deprecated status over to HTML5 where it is now obsolete and non-conforming.
Ref: http://www.w3.org/TR/html4/present/graphics.html#edef-CENTER.
And this portion of the spec talks about deprecated elements: http://www.w3.org/TR/html4/conform.html#deprecated
A deprecated element or attribute is one that has been outdated by
newer constructs. Deprecated elements are defined in the reference
manual in appropriate locations, but are clearly marked as deprecated.
Deprecated elements may become obsolete in future versions of HTML....
This specification includes examples that illustrate how to avoid
using deprecated elements. In most cases these depend on user agent
support for style sheets. In general, authors should use style sheets
to achieve stylistic and formatting effects rather than HTML
presentational attributes. HTML presentational attributes have been
deprecated when style sheet alternatives exist.
There is no immediate risk in using a deprecated element. The user-agents should continue to support deprecated elements for reasons of backward compatibility.
However, The risk you take with using a tag which was deprecated in 1999, is that there may not be much time left when this gets from "deprecated" to "obsolete".
And from the ref above:
An obsolete element or attribute is one for which there is no
guarantee of support by a user agent. Obsolete elements are no longer
defined in the specification, but are listed for historical purposes
Important:
As of October-2014, the center
tag is now obsolete and non-conforming in HTML5.
Ref: http://www.w3.org/TR/html5/obsolete.html#obsolete
The risk you take with using a tag which is obsolete and non-conforming, is simply that your website is well, obsolete and non-conforming. Also, any-time an update of a modern browser happens, it may render your website with presentational issues, unless proper doctype is included.
Summary:
While there is no difference, and may not be for some foreseeable future owing to backwards compatibility, it is better to start slowly phasing out such elements and that is what deprecated means (to wean). Where-ever possible, update the code to conform the latest spec.
.