If anyone is looking for some possible ideas (note that for many of these, one or both pokemon may have multiple niches, and they are being compared in one niche):
Cresselia vs Mew as bulky Psychic supporters.
Bisharp vs Metagross as physical attackers immune to Intimidate.
Whimsicott vs Sableye as Prankster abusers.
Ludicolo vs Rotom-W as offensive rain counters.
Jirachi vs Amoonguss as Rage Powder/Follow Me users.
Scizor vs Breloom as powerful priority users (yes I know about Bisharp but I feel Bisharp is quite different).
Reuniclus vs Chandelure as offensive Trick Room users.
Heatran vs Volcarona as sun sweepers.
Mamoswine vs Cloyster as Scarfed Ice types (since someone mentioned Scarf Mamoswine in the general thread it might be a good idea to discuss the pros and cons).