Dire is definitely the superior draft, both in lane-counters and late-game prescence. Of course, we're assuming everyone is playing intelligently here.

Lanes:

Batrider can have prescence at a further range than Lion's stun, while SB can't without being succeptible to Rubick's, making bat the superior offlaner. SB is going to get starved, and Batrider can avoid Jugg's insane level-6 damage with omnislash, preventing him from snowballing. Pretty much the only thing that can catch Bat is a really solid post-6 gank from Storm.

Mid is pretty much going to be a farmfest, since neither party will be able to confidently kill the other for the laning stage. Storm has a slight advantage here because of his higher gank-potential, but he does not want to let OD freefarm, because that can get very scary very fast.

Doom's ability to jungle gives Dire an additional advantage, at no cost since PA is absolutely safe with just Rubick.

Late:

Radiant has Zeus and Lion to nuke down PA, so she's going to have some serious trouble unless she builds tanky and Rubick gets a pipe - and even then, PA is pretty heavily countered here. Still, even without her, the Dire still have OD, who hits like a truck, and Doom, who does some decent auto-damage too. Doom ss needs to be dropped on Storm every time, since he's the biggest threat once Lion and Zeus blow their nukes, and with Bat, Rubick, and Orchid, Dire have more than enough of an arsenal to keep Juggernaut from getting too crazy, while Radiant, with storm out of the way, only has sb, who can be predicted and countered by a self-prison from OD, and Lion, who will most likely be out of position after blasting PA, but could potentially land a lucky stun on OD too.

Overall, Dire has the advantage. Sorry, dude.