How the two rules work
Naismith's rule comes from an 1892 trip report by the Scottish climber William Naismith: allow an hour for every three miles on the map, plus an hour for every 2,000 feet of ascent. The metric version is 5 km/h plus an hour per 600 m. Eric Langmuir later added corrections for descent: take off 10 minutes per 300 m on gentle slopes (5° to 12°) and add 10 minutes per 300 m on steeper ones.
Tobler's hiking function (1993) turns slope into speed: W = 6 e−3.5 |S + 0.05| km/h, where S is the rise over the run. That gives about 5 km/h on the level and a top speed of 6 km/h on a slight descent of 5%. Off paths, Tobler multiplies the speed by 3/5.
Why they disagree
Naismith charges a fixed hour for every 600 m of climb, however steep. Tobler's speed falls away smoothly with steepness, so it is brisker than Naismith on moderate climbs and much slower on very steep ground. Downhill, Tobler slows on steep slopes, while Langmuir's gentle-descent credit can imply very fast walking near 12°. Where the two differ a lot, plan on the longer time. Both give moving time for a fit walker in good conditions.
Typed totals or a GPX file
With typed totals we assume one even climb and one even descent at the route's average grade. A GPX file is better: we smooth its heights over about 100 m, so GPS jitter does not inflate the ascent, and judge every short step on its own slope. Your level-ground speed scales both rules.