Yes BITS Pilani has a brand value of its own and a BITSian is always known to stand apart from the crowd. BITS has a reputation if you apply for higher studies in foreign universities and when companies are concerned there are some companies in foreign who prefer BITSian over IITian because BITSian are known to have a good overall personality. And BITS itself follows education system which is closely connected to the foreign universities. So to conclude BITS has a reputation of its own which no where lags behind old IITs.
As far as the three BITS campuses are concerned there is hardly any difference and you are anyways given a BITS Pilani degree.
In fact the new IITs may not have a strong reputation in foreign . BITS stands at par with the old IITs