*Technically* neither is correct. The appearance of "square" versus "round" is caused by at least 2 other issues: Dot pitch (possible shadow mask layouts) and Refresh rate.
PC based monitors have tubes with tighter dot pitches than "TV" tubes.
Comparison: .24-.28 dot pitch is common on current PC monitors, while MOST TV's and arcade monitors of the 80's have a dot pitch of around .72 to .92.
PC monitors run at a minimum of 31.5 KHz horizontally, most MUCH higher. TV's run at a maximum of 15.75 KHz horizontally.
Therefore, if you compare the size of the "hole" in the PC monitor with that of a TV, and combine this with the fact that the scanning is done twice if not three or four times faster, you can see the PC monitor has tighter control over how small the dot is drawn. A TV tends to have dots "bleed".
In most cases, this is a VERY good thing. If you've seen some of the newer LCD's with TV tuners or even gas-plasma TV's (and to a slight extent pure-flat TVs) you will notice that the edges of things are now TOO crips. TV works on the fact that your eyes blend things together (e.g. 30 frames per second, interlaced) and if pixels didn't bleed then you'd find yourself noticing way too many problems with your signal, dot crawl, etc...
Of course if your email text was smoothed on a PC monitor, that would be VERY annoying. Pictures or LARGE text is fine, small details is not.
I can say that the original PC VGA monitors (or even back to CGA which were the same as a TV as far as refresh rates go), when dealing with much higher dot pitches and much lower refresh rates, the pixels did tend to be "round". Some of the best 13" PC monitors to hack for use in cabaret video game cabinets are the earlies VGA ones due to dot pitch (though very sharp, still had arcade feel) and refresh rates. After a year or so, they stopped being compatible at the low rates at the same time they drastically improved dot pitch from .52/.42 to .32/.28
Also remember arcade monitors (low res--e.g. the classics) were 320x240 resolution. TV is higher than that. Basic PC monitors are 640x480... 4 times as many dots on the screen. Smaller dots make things appear squarer/cleaner edges than old arcade tubes.