An enlisted Naval serviceman was paid anything from $80 to $213/month, depending on rank and service. I can't find a clear US record, but the Canadians had the lowest (non-training) telegraphist grade as an Able Seaman, and this seems to be at the E-3 level; so by analogy say $100/month. To make it directly comparable to civilian pay we need to account for board and lodging; where the Navy didn't provide these our E-3 would get an allowance of $45 (lodging) and $2.25/day (food) - so say $112.50 allowance, for a total of $212.50.
This report will contain more information than you could possibly want on wages by grade & year for Western Union employees, including discussion of the major pay discussions. Based on Table 2a, a mid-range morse telegraphist could expect $1.24/hour in 1948, $1.41 in 1951, and $1.54-1.69 by 1953.
As an aside, it's worth bearing in mind that unionisation in the industry seems to have begun well before the 1950s (there's some fairly extensive discussion here), so the postwar activity won't reflect the improvement over an entirely non-unionised starting point.
So, how do they compare? In the Navy, assuming he had to find his own bed and board, he'd get $212.50, plus $9 sea pay if applicable, and a further $45 hazardous-duty pay if he did submarine or aviation duty. Or, he could go into civilian work and get about $230/month (five days a week for eight hours at a time), more with overtime or longer hours (not sure if a five, six, or five-and-a-half-day week was standard then). Civilian pay looks a bit better, but not overwhelmingly so.