Hmm, this is hard but it would have been way interesting if it was Alien X vs the TARDIS. To stay on-topic I would say the Doctor, why? Because I have always imagined the Doctor being chased by some hunter (just like the first ark form Ben 10: Omniverse) and being able to resist, adapt (I'm assuming the confrontation is not taking place on open field, the Doctor would have somewhere to hide, while planning) and (I'm also assuming we're talking here by 10-year old Ben since you specified the aliens from the classic series) we shall not forget that the omnitrix will discharge at some point and that will be the moment when Ben will lose and even if he catches the Doctor he will make the Doctor regenerate and in the next few hours we'll basically be invincible because his cells will still be regenerating as seen in The Christmas Invasion or Let's Kill Hitler (assuming Ben will not interrupt his Regenerationn process because of his habit of assuming he won in an arrogant way and not caring if the enemy is truly finished), however if we're talking about Ben from Ben 10: Omniverse, we'll be talking about a better Omnitrix and an experienced Ben that will change the final equation, I'm not up-to-date with Ben 10: Omniverse so I'm not sure how the Omnitrix lasts.
Winner: The Doctor (against 10-year old Ben, not sure against 16-year old Ben, if the Omnitrix doesn't discharge, Ben will be winner 100%, but I'm not sure how the Omnitrix works in Omniverse so I can't tell)
Bonus: Like I said earlier, Alien X, or Clockwork, even Wildmutt (and his ability to sniff to find someone) there are lots of aliens that can outrun the Doctor, it also depends on where the confrontation takes place.
Like I said earlier, it would have been way interesting between Alien X and a Bad Wolf-like Doctor (with the power of the TARDIS).