Ubuntu Manpage for rsyslogd says this

... First of all there has been a systematic attempt to
insure that rsyslogd follows its default, standard BSD behavior...


rsyslogd should be able to use a
standard syslog.conf and act like the orginal syslogd. However, an
original syslogd will not work correctly with a rsyslog-enhanced
configuration file. At best, it will generate funny looking file names.


The second important concept to note is that this version of rsyslogd
interacts transparently with the version of syslog found in the
standard libraries. If a binary linked to the standard shared
libraries fails to function correctly we would like an example of the
anomalous behavior.

So rsyslogd is not very much different from syslogd. Then why do we need rsyslogd?

This page provides a comparison chart rsyslogd vs. syslogd-ng

This blog post explains why a second syslogd?. Excerpts from it:

• .. So one reason the world needs another syslogd is that it needs another major player in the *nix space. I honestly believe there is none except syslog-ng..




• .. have you noticed that syslog-ng has become dual-licensed? There is the great GPLed open source release and the even greater "Premium Edition", which cost money. Only the premium edition offers features like native database and SSL support or queued syslog sending..




• .."Stop", I hear some say, "syslog-ng is GPLed, so we can take that source and implement the missing features". Of course you can. But do you think Balabit will actually include your patches? I guess we can agree on "nope". So you have just forked from syslog-ng ... and proved my argument that the world needs another syslogd..




• .. So - why does the world need another syslogd?
  
              It needs one that aims to be a real major player, being installed on a lot of systems. That will help to get the best out of syslog technology (and in the long term the best of logging at all). Either in its project itself of by driving competitors to be better than it. A new major player will prevent monocultures and provide a rich freedom of choice. That's why the world needs it.