Yes, shx fonts are legacy.
But as to which to use depends on the font face you wish to portray yourself with.
Keep in mind:
shx fonts, being pen plotter vintage, don't proportion as well as ttf fonts. The bigger they get, the thinner they look.
Some shx fonts countered this by having additional lines for some of the characters' definitions, like architxt.shx, to "fatten" themselves up.
But this can bite you on the smaller text sizes, since the additional lines are closer together at the same pen line width.
If you're OLEing in Word or Excel, do you want the remainder of your plot to match in appearance? If so, it's ttf.
Same is true if you're data linking to Excel in LT tables since the font used is from the spreadsheet and not the font set in the table style.
Dean is correct on performance, especially for some ttf files.
The ttf "CountryBlueprint", a for legacy architectural "handwritten" font, has pathetic performance.
Other ttf's, like Arial, work just fine.