Who's a better fighter?

Shyvanna is naturally tanky and works well with Attack Speed, has an easy time getting to the backline and is mobile.

Gangplank is super bursty and long-ranged with his barrels, and is also mobile, but provides more CC to the battlefield.

Mord is in a weird spot right now, but he's really good for counter-engage and taking objs i.e. drake. He's VERY situational.

There isn't a BEST fighter. They all do things differently but I'll give you some insight on the three.

Mordekaiser's a beast when up close and shines in team fights/skirmishes due to his durability and insane damage. He's really immobile and has no forms of CC thus making him really team reliant. But oh boy, if he gets into Melee range better hope they're wearing their brown pants 'cause he obliterates anything in close quarter combat. He's usually played bot but Riot's looking into making his Solo laning better so he'd be a great filler pick if your team lacks a durable carry. Also, he's Metal. 'Nuff said

Gangplank is a great split pusher and has amazing map presence with his cannon barrage. His team fighting and skirmishing relies on good Barrel placement but he can single-handedly turn the tides (hue) of battle with his powder kegs. He's more of a farm reliant champion and skirmisher rather than an all-out duelist/carry like for example Morde or Jax

Can't say much about Shyvana but she's also a Juggernaut like Mordekaiser, often played in the jungle due to her scaling so well with items (sated for example) farming it easily and acquiring big items fast. She's a great duelist and split-pusher and a very disruptive team fighter that get's really tanky and deals a shitload of damage.

Just my two cents though, I personally choose my champions based on their theme/voice rather than their overall niche in the game :P

My Dad > Your Dad

Shyvanna is a jungler/top laner who farms super fast, can build very or glass and do a lot of damage either way, and is great at counter engaging (not so much at initiation).

Gangplank is a well rounded top laner who can probably go even with anyone if he plays safe due to his ranged waveclear barrels and orange to prevent being locked down by only one cc. He also has global presence with his ult so even while being passive in lane and farming or splitpushing he can contribute to plays in bot lane or elsewhere.

Mord is neigh impossible to deal with at melee range unless you are so far ahead of him that its ridiculous. He plays botlane as a melee replacement adc and his great strengths are his massive auto attack damage (I'm talking taking 3/4 of a champions hp in one auto if the conditions are met), being hard to kill because of his shield which regenerates whenever he does damage, and his ultimate which makes a clone of an enemy if you kill them while ulted (allowing you to have essentially 2 adcs in the ideal case).

They all play differently and have differant specialties, and even play different lanes with mord bot, gp top, and shyvanna jungling usually.

If you can't gank a Gangplank you can't really shut him down. A competent Gangplank will drop a barrage on a skirmish or fight in another lane just to nab an assist or a lucky kill. In addition, pushing him to his tower at level 2 or beyond is begging him to get easy Silver Serpents. He's like the Karthus of top lane in that regard, and he has amazing sustain if you're frugal about your oranges and mana. Offensive builds (I.E. Critplank) resemble a Master Yi without invulnerability frames but occasional access to a long-range auto. Whereas Defensive Gangplanks (with Spirit Visage) is amazing at light skirmishes and/or darting in and out of combat, and unless hyper-focused can regen his way back with a barrel of oranges.

Since they often have strong map awareness, it can be tough to gank them post-6 when they start paying MUCH more attention to the minimap and looking around for easy kills/assists, since they get the time to do that with their barrel waveclear.

Be warned, too. A Gangplank can steal Dragon/Baron with their barrels or ultimate.

The playstyles are quite different (and personally I would rather ff than build a single tank item on him).

TL;DR though play Vlad into him and make him (and me) cry.