I just want to know the capabilities.
The 'my guy wins because of theory I made up' stuff is a bit tiresome, and goes both ways. You could just as well argue that Dumbledore, because of all that love, is going to restrict himself to non-lethal means and handicap himself. Or you could argue that they wouldn't fight at all because what would be the point? It's endless.
I'm interested in knowing what happens if the characters try to kill one another - and if one can move at lightspeed as has been suggested in this thread it's a regrettably foregone conclusion.
I didn't make up any theories. I used logic from the manga and anime to back up my claims.
Trunks' abilities are vast. He is a half Saiyan/half human hybrid. Think of him like you would Blade. He has all of a Saiyans abilities and none of their weaknesses(being lust for battle). Trunks, through his heritage was born very gifted. Although the type of power that Trunks came by naturally can be earned through rigorous training(see Goku, Vegeta, and practically everyone in DB), he trained himself to become even stronger. He has super strength(Goku, in his normal form in Z was at 40 tons. Trunks, I'd put at 25-30), super speed(not just linear moving speed, but omni directional speed), durability bordering on invincibility(guns, bombs, missles, even war ships, tanks, etc have been shown to do nothing but piss them off), and his stamina is directly linked to his energy supply(if he were to use all of his power in an attack he'd be helpless. He'd probably die). He can fly, is a great martial artist, and can produce energy attacks of varying degrees of power. These people suggest that he'd need to charge an attack to kill Dumbledore, however, Z Fighters at Trunks' level are capable of very powerful energy attacks with little to no charge time(I can show proof if you need it). Also, Dumbledore is still a regular human underneath his magic and his durability and physical strength would be comparable to one(I can show what Z Fighters do to normal people too if you need it). They can also sense life force/energy and deflect energy attacks.
Now, having said all of that, Trunks can also become a Super Saiyan. That raises all of his abilities by 50 times. Don't stop there, he can also reach Super Saiyan 2. That raises his already raised abilities by 2 times. Meaning he can become 100 times stronger than he normally is. Z Fighters have been known to move so fast that even their own super powered allies can't trace their movements. As I've said, there is proof of Z Fighters surviving in space unaided, however, nothing in the manga or anime has directly said that this is an ability. So I can't definitely say that Trunks could do so. As seen in my videos and other's video, Trunks can completely withstand and even deflect attacks powerful enough to destroy the planet.
Their naive assessment on Trunks monologing is somewhat true. Z Fighters talk a lot, however, Trunks has also been known to not play around and get the job done(I can provide evidence of this as well). Also, they're right in saying that Trunks wouldn't intentionally kill bystanders, but he definitely wouldn't mind fighting Dumbledore, to his fullest, in front of them. So if they were to fight, all of these spells, curses, and charms that Dumbledore would use, he would first have to hit Trunks with. Now, if Dumbledore can cast these attacks in, let's say a millisecond, he very well could beat Trunks. Assuming that they are hax abilities that work the same on any and everything and if that's the case, neither of these characters belong in tournaments like these to tell you the truth. Trunks has even faced and defeated a wizard in his universe. A wizard that Dumbledore supporters(really Trunks/DB haters) would say is weak and a fool. I've already posted what that wizard can and has done.(I'll show you a video if you need it.) Dumbledore, on the other hand, has never faced anyone like Trunks.
Unfortunately for my beloved Z Fighter, he is a good guy at heart and if this were a random encounter, he would not outright attack Dumbledore(a very strong argument could be made that this applies to Dumbledore too). If one went strictly by abilities and feats, however, Trunks would win.