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the battle takes place in a deserted island

The best version of Jak?

Jak won't get enough good shots at Sonic.

But what do they have with them?

Ehh...Sonic has this match. A simple Lightspeed Attack would put Jak down for the count...well maybe not one but Sonic wins none the less.

I believe at least Dark Jak would be capable of pulling it of

I however knows very little about Sonic

They can both win, IMO. Jack has some neat forms and a time spell that can counter Sonic's insane speed. I'll go with Sonic though.

Sonic also has Chaos Control which allows him to control time and space. Jak's time spell wouldn't help him much here.

sonic has his Homing attacks, Lightspeed Attacks etc. and its dark jak

Shadow has Chaos Blast and Chaos Spear.

Sonic has never been shown using those attacks. Sonic has Sonic Wind and the Lightspeed Attack but only Shadow has been shown to use Chaos Blast and Chaos Spear. But Sonic still has his Super Transformation and Darkspine Transformation to counter Dark Jak even if the going gets tough but normal Sonic alone is more than capable of taking out Dark Jak.

As I said, I know little about Sonic so I will keep myself quiet trough the fight

Sonic speedblitz.

jak ain't gonna sit there and let sonic beat him up his gonna take out one of his guns and start shooting his ass down

Sonic moves WAAAAY to fast for Jak to get a clear shot. No matter what Jak does he is a sitting target because at Sonic's speed Jak wouldn't be capable of finding shelter or anything plus with time frozen (Chaos Control) he IS a sitting duck.