Regardless of style points, Kaine wins strategically because

[yellowcanine]

1) He effectively defended Clinton and Pence did not effectively defend Trump
2) He hit the tax return/conflicts of interest issue hard and Pence had no rebuttal.

The first point is a no brainer for a VP candidate - That is the number one thing they have to do.

On the second point, my guess is that this was driven by focus group polling of undecided voters.

Undecided voters for the most part do not watch VP debates. So what they will see are the highlights - over and over again. And those will be brutal for Trump/Pence. Clinton gets a small bounce in the battleground states I think - a point or so.

[C_U_L8R]

1. Someone put it well on another thread

Pence looked dashing while he threw Trump under the bus.
Kaine took great joy at driving the bus over Trump, maybe too aggressively.
Any way you slice it, the net loser is Donald Trump

[imaginary girl]

3. comparison

I'd rather have Maine's aggressive approach than Lieberman 's. Remember that? Kaine doesn't need to be likeable. He needed to defend HRC and attack Trump.

[C_U_L8R]

4. Ugh, Lieberman

That guy was the worst.

[imaginary girl]

6. I know! He was so frustrating! n/t

[yellowcanine]

5. Yes. Pence does not really want to be VP. He wants to be POTUS.

If Trump were to win, he knows he would likely never be POTUS unless Trump gets impeached, resigns or dies in office. Because Trump would be a 1 term failed president and Pence would go down with him. And if he did inherit the office, he would likely only get to serve out the term of a disgraced President.

[uponit7771]

2. While Pence speaks of whipping Mexican things out Pence didn't want to defend Dumbass Donald

[kurt_cagle]

7. Significantly, the media, outside the talking heads, agree

Pence was in an indefensible position - he either went all in with Trump and risk going down in flames with him, or he takes the chance to appeal to the evangelical base at the risk of appearing disloyal to Trump. He did the latter. Focus group, social media and even some of the bigger media outlets are recognizing this.

Trump's support is drying up. The tax scandal(s) are taking their toll, and his remarks about veterans may have lost him many votes there. The evangelicals were looking for Trump to somehow, miraculously, turn into a saint, but child trafficking allegations may be the final straw for a lot of them, and what Pence did tonight was to say "Look, we lost that round, but I can give you a win in 2020". This leaves the alt-right.

The election won't be over for another month, but the anti-Hillary forces are increasingly shooting blanks. Even if something calamitous happens at the final two debates, they will be much less heavily watched. I think it's over, except for the voting.