Gym Leader + Elite 4 teams and levels are also different on Yellow compared to Red/Blue. Many of them modeled after the Anime as you'll see below. Warning: Long post + Commentary ahead.
Brock: Geodude(level 10), Onix(level 12).
They're 12 and 14 respectively on Red/Blue. Consequently, Geodude doesn't know Defense Curl, making taking him down with Normal types relatively easy.
Misty: Unchanged
Lt.Surge: Raichu(level 28).
A solo powerhouse with an Improved Moveset of Mega Punch/Mega Kick/Thunderbolt/Growl. Compare that to a team of 3 Electric types of Voltorb(level 21), Pikachu(level 18) and Raichu(level 24) with bad movesets to deal with Grass/Ground types.
Erika: Tangela(level 30), Weepinbel(level 32), Gloom(level 32).
Higher in level compared to her Red/Blue team(level 24 and 29 respectively) but her team on Red/Blue was fully evolved. Movesets on Yellow are different with the biggest difference being Tangela's. Tangela gains Vine Whip and Erika's signature move in Mega Drain to go with Constrict and Bind. Weepinbel retains Wrap, Sleep Powder and Razor Leaf but dumps Poisonpowder for Stun Spore. Gloom retains Petal Dance and Sleep Powder but drops Mega Drain and Poisonpowder for Acid and Stun Spore.
Koga: Venonat(x 3; Levels 44, 46, 48), Venomoth(level 50).
Huge change from his Red/Blue team and arguably worse. They may be of a higher level but Bug types are notoriously easy to defeat and one could argue Koga becomes a Bug Gym Leader in Yellow... Unlike his Red/Blue team though, they **ALL** know Toxic and Psychic, making rolling with a Poison type like Nidoking against him risky. His first Venonat has Tackle + Seep Powder, 2nd with Psybeam + Supersonic and 3rd one has Sleep Powder and Double Edge. His Venomoth has Leech Life and Double Team, with the latter move being one to worry about since Evasion can be a royal pain.
Sabrina: Abra(level 50), Kadabra(level 50), Alakazam(level 50)
Sabrina has Pokémon of a much higher level with the latter two being dangerous. Abra is the oddball knowing only Teleport and Flash so he's one you can actually setup on if you wanted to. Just be sure to put him to sleep or have some X-Accuracy ready to undo Flash debuffs. Kadabra swaps Disable and Psybeam for Kinesis and Psywave to go with Psychic and Recover. Her ace Alakazam retains its Red/Blue moveset with one major upgrade: Psybeam -> Psychic. Her ace means business now.
Blaine: Ninetales(level 48), Rapidash(level 50), Arcanine(level 54)
While his team is smaller in Yellow, they're of a much higher level. Ninetales isn't even on his Red/Blue roster and sports Confuse Ray, Quick Attack, Tail Whip and Flamethrower. Rapidash replaces Tail Whip with Take Down, tapping into its decent Attack Stat. Arcanine replaces Roar and Ember for Reflect and Flamethrower, making his Ace actually decent.
Giovanni: Dugtrio(level 50), Persian(level 53), Nidoqueen(level 53), Nidoking(level 55), Rhydon(level 55)
Debatable as to whether his Yellow team is an improvement. Dugtrio is up first and its moveset is weaker compared to Red/Blue with Sand Attack, Dig, Earthquake and Fissure. Meaning he lacks anything to handle Flying Types so Gyarados completely walls him(shame there's no Dragon Dance...). Persian was completely missing from his Red/Blue team and gives his team something of note because STAB Slash + Double Team is straight up crazy if you let it setup. Has Screech and Fury Swipes to round out its moveset but is powerless against Gengar. Nidoqueen retains Tail Whip and Poison Sting(why I dont know...) but swaps Scratch and Body Slam(why... its good ugh) for Double Kick(wtf) and Thunder(Thunderbolt is better due to accuracy). Nidoking dumps everything but Thrash from its Red/Blue moveset and replaces it with Earthquake(good), Leer(ugh...) and Thunder(again Thunderbolt is better for accuracy). His ace in Rhydon dumps everything but Horn Drill from its Red/Blue moveset and replaces it with Earthquake(good), Rock Slide(great) and Fury Attack(ugh... 3 out of 4 is ok I suppose... Stomp or Body Slam would have been better).
Now for Elite 4. Level wise they're the same as Red/Blue but movesets... oh so much better(imo).
Lorelai: Dewgong(level 54), Cloyster(level 53), Slowbro(level 54), Jynx(level 56) and Lapras(level 56)
Dewgong got a nice buff in Yellow by giving it a STAB Water move in Bubblebeam(replacing Growl). Cloyster's moveset is unchanged while Slowbro got a massive upgrade. It retains Amnesia and Withdraw but it becomes a true Water/Psychic type with Surf + Psychic. Let it setup with Amnesia and it hits like a truck. Jynx and Lapras movesets remain unchanged.
Bruno: Onix(level 53), Hitmonchan(level 55), Hitmonlee(level 55), Onix(level 56), Machamp(level 58)
Biggest difference on Yellow are the Onix movesets. Both Onix get STAB Rock **AND** Ground moves with first one getting Rock Throw/Dig while the 2nd gets Rock Slide/Earthquake. They round out things with Screech and Slam. Hitmonchan's moveset is modestly different. It swaps Mega Punch for Fire Punch and removes the useless Counter for Double Team. Hitmonlee is similar in that it dumps Focus Energy and Jump Kick for Double Kick and Double Team. Machamp drops Focus Energy and Fissure for Strength(an HM move!!!) and Karate Chop(high Crit so it can hurt).
Agatha: Gengar(level 56), Golbat(level 56), Haunter(level 55), Arbok(level 58), Gengar(level 60).
Yellow differences start right off with the first Gengar. It retains Confuse Ray but replaces Hypnosis, Dream Eater and Night Shade with Lick, Mega Drain, Substitute. The latter two can catch people off-guard and Mega Drain is meant to counter Ground types. Golbat on Red/Blue had two Confusion moves in Supersonic and Confuse Ray. Yellow dumped the latter along with Haze for Leech Life and Toxic. Haunter had its Night Shade replaced with Lick, otherwise same moveset as its Red/Blue counterpart. Arbok replaced Bite with Wrap and while you may think thats a downgrade, Wrap is an underrated Trap move in Gen 1. When used on Paralyzed opponents, you can't move. If you're Poisoned but outsped, you'll be bleed HP until fainting. The final Gengar swaps Toxic and Night Shade for Hypnosis(makes sense with Dream Eater... Red/Blue one had it but no way to put people to sleep) and Psychic.
Lance: Gyarados(level 58), Dragonair(x 2; level 56), Aerodactyl(level 60), Dragonite(level 62)
No change on Gyarados, although I'd argue Surf > Hydro Pump. His Dragonair movesets change a lot in Yellow though. They both retain Hyper Beam but the first one has Thunderbolt/Thunder Wave/Slam(replacing Agility/Dragon Rage) while the second one has Wrap/Bubblebeam/Ice Beam(replacing Agility/Slam/Dragon Rage). Aerodactyl retains Hyper Beam but swaps out Bite/Take Down/Supersonic for Fly/Wing Attack/Swift. His ace gets a big upgrade by dumping Agility/Slam/Barrier for Blizzard/Fire Blast/Thunder to go with signature Hyper Beam. All risky moves but they hit like a truck.
