Ooh a tough matchup here.
Having run multiple nuzlockes across multiple different versions of the Kanto and Johto sagas, I gotta say both these third gym contenders can be tough contenders if you aren't prepared.
With Lt. Surge, while his Raichu does know Quick Attack in FRLG which can trip up an unsuspecting player, if you have a ground type that's its only offensive move. For nuzlockers specifically, depending on your game version you'd have had roughly five ground type options leading up to this. Right before Mt. Moon, you can encounter either of the Nidorans which thanks to the Moon Stones in Mt. Moon could easily be fully evolved by the time you get to him. Geodudes are plentiful in Mt. Moon as well and Diglett's Cave is right next to Vermillion City offering plenty of Diglett and if you're lucky maybe even a Dugtrio. And then if you're playing Leafgreen, you also have the option of a Sandshrew in some of the earlier routes. All in all, while their movesets might be rather lacking, the fact that you get the TM for Dig before the battle as well can also prove useful even if you manage to fail all these encounters, with plenty of pokemon able to learn it as well.
Talking battle strategy wise, Whitney is a lot more difficult to counter, especially in the remakes. First off, as previously mentioned, she's a normal type gym leader, which means her only weakness is fighting types. While normally this isn't too much of a problem, in Johto your only fighting type optiona up until now are Machop and Heracross. Arguably, the easier is the machop. They aren't available in the wild until much later but you can trade for one in the department store of Goldenrod. This is a lot tougher of a task in nuzlockes though, as it requires a drowzee for the trade, a pokemon only available on two routes, both of which have plenty of other pokemon. So if you fail those encounters, no Machop. Heracross are a bit trickier, since you need to headbutt trees to obtain one. Generally the odds of one are fairly low, and unfortunately in Gen 2 it learns no fighting moves naturally until level 44. It is a bit more of a viable option in Gen 4, but this is likely due to Milktank getting a buff from the ability scrappy.. While geodude and onix are available earlier on as decent walls to stall out the team, offensively neither pokemon is all that great so it'll make for a long stall out match against that miltank that could go horribly wrong if the circumstances aren't just right. There's also the fact that ghosts like gastly aren't a viable option anymore in Gen 4. As mentioned previously, in the remakes, Milktank gains the ability Scrappy. Previously not available in Gen 2, it made pokemon like gastly a bit more of a viable option since it was immune to all of miltank's moves except rollout. Scrappy throws that out the window though, able to destroy ghost types with stomp in Gen 4. So overall, talking from a nuzlocke persective, Whitney is the much tougher fight. And we didn't even get into that nightmare of a Clefairy man.
Gym design wise I will say Whitney's gym is a lot less impressive. It's cute that it's shaped like a clefairy but really the only challenge are the four trainers along the way. Lt. Surge's gym has always been infinitely more frustrating with that two button challenge. Sure sure the second button is always adjacent, but that doesn't mean it's not still hard to try and get every single time. Plus, the gym trainers are actually fairly challenging too to boot.
I also like Lt. Surge's character a lot more than Whitney's. I hate her crybaby attitude and her refusal to give you the badge. Sure she kinda makes it up to you in HGSS but come on man she's a gym leader she can't act like that in a professional setting. Lt. Surge is a lot cooler especially with some of the character development he got in other mediums like the manga. Just overall, a much cooler guy.
So I'll be picking Lt. Surge as well.
Lt. Surge vs. Whitney!
