Alright, i'll give this my best shot...
Mamoswine Or Flygon?
Well, let's see what each of them can do in their respective tier...
Possibly the best counter to any dragon Pokemon, Therian Formes, and top tier threats/walls, such as Breloom, Heatran, Magnezone, and much more things. With a Priority Ice Shard, decent Speed, amazing movepool, ability to run 2 choice sets, wonderful bulk, Can set up Stealth Rocks, and has a decent ability (Thick Fat), you can see why this guy is pretty amazing and can tech you the definition of destruction if you are unprepared for him.
Basically, the Dragon king of UU (Kingdra being the Queen :P). He also can run 2 Choiced sets, has a Scouting move, has one immunity, a-little-more-than-decent movepool, has a godly base 100 Speed stat (which is pretty good for UU), and can hit everything in UU or below (except for Shedinja) for Neutral damage or better. Basically, the harbinger of death if you dont have a Defensive Pokemon.
Realize that both are the top dogs in their tier, and only taken down by few, though that doesn't mean they can't be taken down. Now, for movesets...
Mamoswine @ Life Orb / Choice Band
Trait: Thick Fat
EVs: 252 Atk / 252 HP/ 4 SDef
- Ice Shard
- Icicle Spear /Icicle Crash / Stone Edge
With this moveset, nothing takes a hit from Mamoswine safely. Ice Shard is definitely priority, and EXTREMELY useful for taking things down such as a Dragonite, who is probably at +2 or beyond that. Icicle Spear/Crash are just backup moves when you need to deal a great amount of damage, and would prefer not to rely on Ice Shard's 40 base power. Stone Edge is an alternative if you want to hit threatning Pokemons such as Volcarona. Superpower helps you take care of Ferrothorn, the random Air Balloon Heatran, and other Ice types, in case you didn't pick Stone Edge. Earthquake is STAB, and makes this big boy hit like a Battle Subway train. Great for killing off Magnezone or Tyranitar, or things of that sort. Definitely a top dog (or Mammoth) of OU.
Flygon @ Choice Scarf / Choice Band
__________ Nature (Adamant if using Band, Jolly if you're going for Scarf)
EVs: 252 Spd / 252 Atk / 4 HP
- Outrage / Dragon Claw
- Fire Punch
IMO, 3 best scouter of UU (only below Azelf and Mienshao). U-Turn helps you just deal damage off the start, and helps other team members do their job, seing that nothing(except Shedinja) is immune to bug attacks. Earthquake is really just a good, effective STAB move which lets you hit the scary, sweepers of UU, such as Raikou, Arcanine, Darmanitan, Empoleon, and much more. Outrage, while only hitting opposing Flygons and Kingdra's for Super Effective damage, it hit's anything else that can take or is immune to EQ. However, if you don't want to be locked into one specific move, you can use Dragon Claw. While still doing decent damage, the power drop is noticeable. Finally, we finish off with Fire punch, while helps Flygon form the almighty FireDragonQuake combo that no Pokemon can resist. This gives you coverage against Herracross and Bronzong, which are both pretty popular Pokemons, and still hits things like Shaymin and Rotom-Mow. Definitely a great Pokemon.
Now, if you want to compare one against the other in a battle, it litterally is no contest... Mamoswine can defeat Flygon anyday.
If you are talking about ingame, then really, both choices are fine to use. Mamoswine can take a hit, deliver a stronger one, and does very well due to his typing. And Flygon, on the other hand, is also a good choice. Seeing that Dragon types can hit all but Steel types ingame for neutral damage, Flygon is a good choice, and other dragons aren't a threat if you aren't under leveled.