Hello! I am The Amazing Squid. I'm starting a series in which I pick a pair (oooh alliteration) of magic the characters, and set them up for a fight. Here, we discus who we think would win, disregarding cards.

The very first pairing is

*drum role*

We don't really have much on each for there fighting skills, but I'm guessing probably Tamyio.
I just wonder how Tibalt is still alive after trying to fight Sorin

You'll need to provide more than that. We need the scenario and setting for their fight.
It'll make a world of difference if they're at the Ashmouth or Oboro after all.
Regardless, Tibalt likely has the edge in terms of physical assets, since he actively carouses with a gang of devils and has the tendency to not give a crap about their welfare.
We know nothing about Tamiyo's skills, either mystical or hand to hand, but given her origin, we can assume she has some above average skill. It's also somewhat telling that she travels alone primarily, meaning she's either extremely skilled or she simply runs.

Aside from that, we need to know their individual goals in the fight. If we just toss them against each other, if there is no reason for them to fight, either of them could simply leave and effectively "win" the fight. We need stakes here.

Extra info as requested from the eldritch librarian:

For the lands, I don't want to make it specific to one of there colors, for obvious reasons, so I'm going to go with salt flats. Tamayo went there to study. Tibalt was there to...gather salt. Assume that tibalt made the first move, and tamayo was acting in self defence.

Tamiyo just walks away and Tibalt goes off in a murder spree on easier targets. There.

Tibalt still has the edge since he can draw black from the flats. He does use black after all.
Anyways, we know physically Tibalt has a knife, but Tamiyo appears to travel unarmed. Given her people though, she's likely to be trained in hand to hand.
As far as their spell repertoire goes, I think Tamiyo has the edge given Tibalt's extremely narrow focus, but we honestly can't be sure what Tamiyo is properly capable of since the exact nature of her casting is still really nebulous.

This is wrong and you know exactly why.

EDIT: that was rude. What I meant to imply was that since this is contemplating who would win in a fight, it is implied that there is an actual fight, in which there is a winner.

Tibalt loses, because he's being played by John, and John's a scrub.

Okay, so here's my approach to this question.

Things I'm not going to do:
-Think long and hard about my answer.
-Draw upon a deep and nuanced understanding of the characters and their established competencies.
-Use math.

Things I am going to do:
-Take the first thing that pops into my head, and run with that sucker.

Now that we're clear on my method, here's my verdict - Tamiyo takes it in a surprise knockout.

Why? Because, while outward signs would suggest that Tibalt has a severe badditude advantage, I'm going to say that Tibalt is a bully when you get right down to it. Sure, he tortures and defames and mangles, but he picks on the weak. And, if movies about high school have taught me anything (and, other than that the way to win a girl's heart is to stand outside her window holding up a boombox for the duration of "In Your Eyes," they haven't), it's that (1) bullies lose their nerve when someone fights back and (2) the least likely person to fight back always turns out to know karate or something. (Or maybe I'm just thinking of Sidekicks. God, did I love Sidekicks.)

Anyway, Tibalt starts the fight because he thinks this dainty-looking lady is a pushover. Instead, she roundhouse kicks him in the face. Tibalt makes a face like Joe Piscapo does in Sidekicks when Chuck Norris beats him up, and then he runs away.

The winner: Tamiyo in the first round.

God, now I want to watch Say Anything and Sidekicks.

EDIT: I always forget what a marvelous thing the internet is. See the 2:40 mark for my vision of how this fight goes.

OK my views on the topic:
I think orcish librarian makes a good argument about the bully vs. jedi type thing. Though based on what we know about tamayo, she is a mind mage of some sort. More of the draw cards type. It also seems that she is an explorer, and researcher. The stereotypical "researcher" type tends to be peaceful. This combined with her "draw cards" type of magic, and the scenario I set with her defending herself, its seems that she would probably stall as long as she could before ending him swiftly (possibly with mind magic). If it was mind magic though, it might not work. Chandra's chaos was enough to stop jace from hacking her, & tibalt is way more insane then chandra.

Why would you make someone choose between the two sexiest printed planeswalkers!?!

She isn't. That's Jace's schtick. It's hard to nail down what Tamiyo's discipline is, but they wouldn't cross the streams like that. Not without a REALLY significant difference. See: Ashiok vs Jace.

If anything, I'd put Tamiyo likely as a counter mage. She does some things, but it looks like her first instinct is to keep YOU from doing something.

Tibalt is likely to get the jump on her since he doesn't really require a reason to attack anyone. The T man just kind of drops by and starts wailing on you.
I'd rather assume though, that both characters are possessed with the same determination to kill each other before the fight even starts. Just plop them into the ring Streetfighter style, you know? I think Tamiyo would take the match. We know that Tibalt is newly ascended, and while details on Tamiyo are scarce, she seems a lot more professional.

OK so this is the official end of the first installment of "versus!". I have deemed it successful, so part two will be coming soon.

Do you take vs requests?
Also you could run these as polls.

OOOOOOOOh both good Ideas. Just place your requests here, though there probably come up as the one after the next one (if i deem the reasonable)

Jaya vs Chandra in the furnace of rath.

Garruk vs sarkhan on the top sphere of phyrexia.

Malfegor vs Avacyn, on let's say Mercadia.