Because most Pokemon increase their stats when evolving, you would not normally see a not-fully-evolved competitively. The most common exception to this is caused by pokemon holding Eviolite:
Effect: Raises the holder's Defense and Special Defense by 50% if the holder is not fully evolved.
It is important to remember that this will multiply not only base stats, but the final value, which includes IVs (Individual Values) and EVs (Effort Values). This is obviously most effective for acting as a wall. There are multiple pokemon which see competitive usage with Eviolite, but most notable are Chansey, and Porygon2. Dusclops, Doublade, Scyther, Golbat, Magneton, and Gligar may also use it well.
For numbers lets look at smogon's OU builds for Chansey and Blissey. Plugging the level (used 50, per VGC), EVs, nature and max IVs into a calculator (links on names below) we get:
HP Atk Def SpAtk SpDef Spd
Blissey: 331 27 68 95 187 75
Chansey: 326 22 62 55 157 70 (without Eviolite)
Chansey: 326 22 93 55 235.5 70 (with Eviolite)
This shows Eviolite Chansey has 137% Defense, and 126% Special Defense compared with Blissey, with 98% HP, 93% Speed, 82% Attack, and 58% Special Attack. This obviously increases survivability, and competitive Chansey would not have a move depending on Attack or Special Attack, so those stats would not matter.
A major downside of using Eviolite is that it is taking up an item slot, meaning no Leftovers or 'choice' items, but many competitions (including VGC) enforce an item clause (no duplicate items), which leaves leftovers for another member of the team.
Threads on smogon and gamefaq cover the eviolite users.
Best Answer
There aren't any Pokémon in XY with changed base stats that require Bank to obtain - all of the ones that were changed are obtainable in XY in one way or another. The full list is below:
Generation 1: 14
Generation 2: 4
Generation 3: 2
Generation 4: 2
Generation 5: 7
Source: Serebii