So, what's the "smarter" way to get from Junction Hollow to Frick Park?. Well, that depends on your preferences, and it raises a lot of questions, even though you've narrowed it to option A or B.
First, I'd say that Schenley & Frick Parks, and adjoining neighborhoods offer much to explore, and East Enders probably all have their little back ways and preferences. However, thinking of closing the loop that you describe, I might also suggest a third option, "A1", through Shadyside to Point Breeze via Mellon Park.
Both options A and B traverse Squirrel Hill - which involves more climbing (think a couple hundred feet), though I think option A would be a little easier, and you would descend the upper elevation (as opposed to the "lower elevation", from the plateau to the river) to Point Breeze on the road, whereas, in option B, you would descend on unpaved trails through the park. Either way, your destination is Frick Park, but the park is huge, and the Squirrel Hill and Point Breeze sections are well removed from each other (topography has as much to do with it as distance).
Option A (or "A1" through Shadyside) to the Point Breeze entrance, allows you to traverse the entire length of the park. You could take the "Tranquil Trail" down, which is direct and very nice, or you could get over to the Braddock Trail, which is less direct but magnificent, imho.
Option B seems to be indicating the Nicholson St. entrance..., in which case, the trails may be a little rough getting down (with some potential for getting lost), however, there's another option too, (let's call it B1)... the Beechwood Entrance at the Frick Environmental Center (Just south of Forbes). From there you could take the gentle Clayton Trail to Forbes (preferably the one that loops to the right, futher from Forbes... I believe it's "Lower Clayton"), then ride a short way across a bridge on Forbes to connect to the previouly mentioned Braddock Trail, which runs behind Regent Square, and goes the whole way to 9 Mile Run.
The most direct, most "park", least "city", would be through Schenley Park and Squirrel Hill, to one of the Beechwood Blvd. entrances.
The most "gracious", would be through Shadyside and Point Breeze to the Reynolds St. entrance. If you go up and down Wilkins, you need to get to Wilkins...; myself, I don't ride 5th Ave., (though I suppose there's the sidewalk). Barring the spiffy "back ways through parking lots" (which is probably what I'd do}, that already puts you on Ellsworth to Amberson, so you're already in Shadyside; why climb the hill (unless you want to)?
If you go through Schenley Park, I'd take Lower Panther Hollow Trail from Panther Hollow Lake to Bartlett St. You can access the lake by crossing the tracks at the end of Junction Hollow Trail, just before it ends at Boundary Street.
See if any of that makes sense or accords with your preferences, then maybe I or others can clarify. Happy riding!