Gangplank is a pirate.
But Pantheon is a spartan...
Looks like traditional choice-choosing methods won't work here!
So instead, let's look at them mechanically.
Each of them are melee characters with a spammable ranged poke/creep killer (targeted, no dodging). So spamable in fact, that sometimes, I forget that they are indeed melee characters.
The normal spot for either one of them is Top lane. This means you'll usually be fighting 1v1 vs another player, and occasionally, will have to fend off two people by yourself, not to mention being the easiest target for your enemy jungler.
(G)Grog-Soaked Blade - Gangplank's basic attacks and Parrrley apply a poison that deals magic damage each second and slows movement speed. Lasts 3 seconds and stacks up to 3 times.
-To be honest, I've never been scared of the extra damage, but having a slow on every attack isn't too shabby. Let's look at...
(P)Aegis Protection - After attacking or casting spells 4 times, Pantheon will block the next incoming basic attack or turret attack.
-Pantheon is one of the kings of tower diving. By playing him well, you've helpped out your jungler already. This will also stave off some harassment. People don't want to get close and break your shield. It helps you win most trades.
(G)Parrrley - Gangplank takes aim and shoots an enemy unit with his pistol. If Parrrley deals a killing blow, he gains extra gold and half the mana cost is refunded. Gangplank shoots a target unit for 20/45/70/95/120 (+1.0) physical damage. If Parrrley deals a killing blow, Gangplank gains 4/5/6/7/8 extra gold and half the mana cost is refunded. Parrrley can crit and applies on hit effects.
-I've seen this ability tear people apart. It does the same damage as your auto attacks + more, and if you use it to farm instead, you're already richer than Ashe.
(P)Spear Shot - Pantheon hurls his spear at an opponent, dealing damage. Pantheon hurls his spear at an opponent, dealing 65/105/145/185/225 (+1.4) physical damage.
-o.0 more base damage, and a higher ratio!? It doesn't apply on hit effects (can't triforce proc with it), and it doesn't give extra gold, so Pantheon has the edge early game.
(G)Remove Scurvy -Consumes a large quantity of citrus fruit which clears any crowd control effects on him and heals him for 80/150/220/290/360 (+1) health.
-Having a healing Quicksilversash as an ability is nothing to laugh at, and is a cheap, early escape from ganks.
(P)Aegis of Zeonia - Pantheon leaps at the target enemy champion and deals 50/75/100/125/150 (+1) magic damage and stuns them for 1 second. Pantheon also instantly refreshes his Aegis Protection.
-!!! You mean you move, deal damage, stun, and block the next attack (and you can do this immediately after the previous block?) Two tower shots, two auto attacks (if they're dumb enough to turn arround after done being stunned). This is pretty cool.
(G)Raise Morale - Gangplank fires a shot into the air, increasing nearby allied champions' attack damage and movement speed. Passive: Gangplank gains 8/10/12/14/16 Attack Damage and 3/4/5/6/7% Movement Speed. Active: Gangplank fires his pistol into the air, disabling his passive boost but increasing his Attack Damage by 12/19/26/33/40 and Movement Speed by 8/11/14/17/20% and nearby allied champions' Attack Damage and Movement Speed by half that amount for 7 seconds.
-Having a team steroid is wonderful in taking objectives. It also gives him stats he doesn't have to pay for. Let's see pantheon top that!
(P)Heartseeker Strike -Passive: Pantheon's basic attacks and Spear Shot gain 100% critical strike chance against targets below 15% health. Active: Pantheon focuses and deals 3 swift strikes in front of him for 13/23/33/43/53 (+0.6) physical damage per strike. Deals double damage to champions.
- FREE CRITS! KS stands for kill secured, remember. Those three strikes help refresh his passive as well.
Well it comes down to their ultimates.
(G)Cannon Barrage -Signals Gangplank's ship to fire upon an area for 7 seconds, slowing enemies in the area by 25% for the duration. Cannonballs rain upon the area, each causing 75/120/165 (+0.2) magic damage.
-Instant AOE slow + somewhat unreliable damage anywhere on the map. Requires good map awareness.
(P)Grand Skyfall - Pantheon gathers his strength and then leaps high into the air, crashing down at the target area a few seconds later. Deals up to 400/700/1000 (+1) magic damage to units at the center (down to 50% at the edge) and slows their Movement Speed by 35% for 1 second.
-Much more difficult to use well, very unreliable damage and slow, but moves Pantheon about the map.
tl;dr: In the end, They're both very good characters. I think Pantheon has more going for him though.