First, Blastoise, Starmie, Jynx, and Vaporeon are all better than both Lapras and Dragonite. Lapras is better than Dragonite, so use Lapras if you don't want to use any of those 4 Pokemon for some reason.
Lapras
Availability: Mid-game (Silph. Co, from a man after defeating rival, level 25).
Typing: Water and Ice is an effective offensive type combination, the latter helping against the former's weakness to Grass. It's great against Blaine, Giovanni, and Lance.
Stats: Attack and Special Attack of 85 are good enough but will make super effective STAB 2HKO some tougher opponents. 60 Speed is slow but is compensated by a hefty 130 HP and good Defense and Special Defense of 80 and 95, respectively.
Movepool: HM Surf and Ice Beam by level will be Lapras's STAB moves. Against opposing Water-types, either Rain Dance + Thunder or Thunderbolt through TMs are helpful. Other options include Body Slam, Confuse Ray, or the situational Perish Song to set a timer on final foes.
Major Battles: Lapras can sweep every fight up until the Elite Four, though it will need an Electric move to handle rival's Gyarados or Blastoise. At the Pokemon League, Lapras shines against Lance and can contribute to Lorelei and Agatha, though it should avoid Bruno.
Additional Comments: A key flaw with Lapras is that it comes later than other Water-types one might want for their team. In addition, it has to catch up in levels, which is worsened by its Slow growth rate. Still, if one is willing to wait and put in some work to train it, Lapras is a solid contributor throughout the game.
Dratini
Availability: Mid-game (buy at Game Corner for 2800 (FR) or 4600 coins (LG), level 18 (FR) or 24 (LG)).
Typing: Offensively poor, offering no STAB for its main Water and Electric-type coverage moves. Defensively good with Electric, Water, Grass, and Fire-type resistances, which are particularly useful against Erika and Blaine, but with a sheer weakness to Lorelei.
Stats: Pitiful as a 300 BST Dratini. Throughout its useful life, Dragonair's low bulk and defenses often result in it being 2HKOed when dealt neutral damage in major battles. Its 84 Attack is its best offense, though it relies on the lower 70 Special Attack. Dragonite's stats are all-around great, on the other hand, assuming you manage to evolve Dragonair in time for the Elite Four.
Movepool: Terrible level-up moveset with only Dragon Rage having relevance. TMs like Water Pulse, Shock Wave, and Secret Power (which can upgrade to Return) are the best moves for immediate use and training. Surf along with the Thunderbolt and/or Ice Beam TMs are necessary for Dragonair to continue to be viable, though if Dratini was bought from the Game Corner, it won't have immediate access to the Game Corner TMs. Dragon Claw through TMs can help Dragonite OHKO Lance's Dragonair.
Major Battles: Struggles against most rival fights and Koga. It is capable of performing well against Sabrina (with Secret Power), Blaine (with Surf), and Bruno (if it knows Wing Attack as a Dragonite). The Elite Four overpowers Dragonair if it hasn't evolved. Other Gym Leader matchups can be improved with the Game Corner TMs.
Additional Comments: Dratini requires significant investment in order to be usable, such as numerous Rare Candies to evolve into Dragonite in time for the Elite Four to compensate for its Slow growth rate. In addition, the line is completely reliant on TMs like Shock Wave, Secret Power, Ice Beam, and Thunderbolt to be viable, some of which won't be available to it immediately due to its cost at the Game Corner. Dratini can be caught at the Safari Zone with a Super Rod, but it is difficult to catch and thus not efficient either.
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