Neither system is better than the other. In some situations, 1x is better, in others, 2x is better. As cassette range expands, effectively because the largest cog is getting bigger, the advantageous of 2x (or 3x) are decreasing. (SRAM just released a 1x12 with a 10-50 cassette, which is probably the nail in the coffin of 2x in the top end gear sets on MTBs).
As a rough starting point, if you are regularly using you lowest gears, and other times your highest gears, a 1x is probably not for you. if you ride flattish terrain, or are a strong rider who climbs well, 1x is a candidate. The NX and XT cassettes are 11-42 giving a gear range of just 380% vs a typical 2x of 11/36 and 24/36 giving 470% (although 11-46 are available giving 420%)
A large reason for popularity of 1x in Mountain bikes comes from full suspension frame builders. By loosing the front shift, they free up space around the already crowded bottom bracket area. This is a very high stress area of the bike, throw in pivots for full suspension and life gets difficult. Removing the derailleur and it goes from 'impossible' to 'nearly impossible' to make a better frame.
Manufacturers love 1x as it lowers the total cost and complexity of an installed drive train, and marketing love it because is something thats clearly 'new' and therefore must be 'better' Meaning there is cost saving to be had, that does not need to be passed on to the consumer as it can be sold as an improvement.
If we put those two aside and consider just an upgrade of an existing frame
- Bigger overall gear range
- Closer spacing between gears (if same number of gears)
- Lower weight
- Linear gears
- Less cluttered handle bars
- Fewer mechanicals - less things to go wrong, less adjustment
Keep a very close eye on costs - upgrading from Tourney means the bike was not really high spec to start with. Its likely a 1x11 gear set will cost more than the bike is worth, and provide no significant advantage over upgrading just the rear derailleur and shifter (Cassette, chain, shifter cables are really consumables).