Nixon would still have been removed from office even if Watergate had happened in the 21st century. The scandal was a major crime and it would be illegal no matter what decade it happened in. Nixon should not have wiretapped the Democratic office because he had no legal reason to do so.
If Richard Nixon had carried out the Watergate Scandal during 2010 or beyond, he wouldn't have been removed from office by Congress. The fact of the matter is that such an event wouldn't have been nearly as shocking to the American people today as it was back then. There's no reason to think he would have been removed.
Nixon did not know about Watergate when it happened, and came into trouble only because he tried to cover up the break ins. There are many instances today of politicians lying or doing illegal things in government, but an impeachment just wouldn't happen - the candidate's party would never allow it.
Consider that we let a President who lied to us in order to start a war from 2000 - 2008 causing over a thousand American deaths, stay in office. A man who gave his donor buddies and their associated firms sweet contracts to furnish that war with everything needed. Permitted him to torture enemy suspects and hold them in prisons without due process. If we let George W. Bush stick around for eight years while doing that, why would we impeach Nixon for a little old office burglary?
If Richard Nixon's Watergate Scandal had occurred in the 2010s, then Congress wouldn't have removed him from office still. Such a scandal would have been far less shocking to the American people than it was when it originally occurred. With that in mind, Watergate wouldn't have been such a contentious issue.