I never really could figure this out myself since the only battle they've had in the actual books is in the fifth one at the Ministry of Magic. If you could make your answers detailed and use evidence from the books in them.
It can be theorized that Dumbledore did NOT consider himself as all that much stronger that Tom.
My reasoning is based on the following paragraphs from "Deathly Hallows" - chapter "King's Cross":
They say he feared me, and perhaps he did, but less, I think, than I feared him.
“Oh, not death,” said Dumbledore, in answer to Harry’s questioning look. “Not what he could do to me magically. I knew that we were evenly matched, perhaps that I was a shade more skillful. It was the truth I feared. You see, I never knew which of us, in that last, horrific fight, had actually cast the curse that killed my sister. You may call me cowardly: You would be right, Harry. I dreaded beyond all things the knowledge that it had been I who brought about her death, not merely through my arrogance and stupidity, but that I actually struck the blow that snuffed out her life.
“I think he knew it, I think he knew what frightened me. I delayed meeting him until finally, it would have been too shameful to resist any longer. People were dying and he seemed unstoppable, and I had to do what I could.
As we can see from the quote:
In the prior war, he ONLY delayed fighting Gellert Grindelwald because he was afraid of finding out his worst fear - that he was the one who killed his sister.
Once the shame of this sad event became less than the shame of allowing Grindelwald committing his atrocities, he went to fight, with no hesitation - despite being equally matched, and barely a shade more skilled. He wasn't afraid of death despite that.
Yet, in BOTH of the Wizarding wars against Voldemort, he never bothered trying to directly fight him until the end of Year 5 when he was forced to, to defend Harry's life.
The obvious objection ("because of Horcruxes, he'd find it futile") doesn't fly for two reasons:
In the First War, he likely didn't know about Horcruxes yet.
Even if he did (or during Second war, when he did), Horcruxes merely prevent Voldemort's soul from leaving the world when his body is killed - meaning that they would NOT prevent Dumbledore from capturing Voldemort; OR from killing his body to give the Order a temporary win, during which they could round up Death Eaters and deprive Voldemort of devoted help in the future; or heck, find and destroy Horcruxes.
The second point also dispenses with the other possible objection ("he didn't do it because he believed in the prophecy, so he wanted Harry to be the one to fight Voldemort"). Same thing - he could, at least, capture or defeat Voldemort temporarily, to give their side more time to find Horcruxes, and spare some innocent lives.
The only explanation I can think of was that Dumbledore thought that Tom was much stronger than him, and thus couldn't risk his life (and thus the chance to find and destroy Horcruxes that was his main task aside from protecting Harry) before all Horcruxes were destroyed.
An additional confirmation is the statement from Dumbledore himself, in "Philosopher's Stone":
"You flatter me," said Dumbledore calmly. "Voldemort had powers I will never have." (Dumbledore to Minerva).
This isn't quite "stronger", but seeing how the only power Dumbledore has that Riddle does not is "love", it's a good confirmation to the theory above.