I think the most important difference between the two different approaches is what the primary motivation behind donating is in each.

With kickstarting a tournament, overwhelmingly what a donor is getting out of it is the fact that the tournament is happening. The role of donation perks isn't to get people to donate in the first place, it's to up-sell people who already would have. The perks are still valuable to the people getting them but they're not the point. Because the model doesn't really stretch the number of people donating (except by making it easy to give money and peer pressuring by showing how many people already have which can be incorporated into dota2 as well) and instead stretches how much they're donating you're looking at fewer donors giving more per person. You're getting about $70 per person donating which is hugely above and beyond what you could ever get with the dota2 method. Also by it's very nature only the kickstarter way can be used to start a tournament, kickstarter is additive and brings you from 0 hype to hype whereas dota2 is multiplicative and brings you from 1 hype to 1.5 hype or whatever.

With dota2 the donors are more customers. They're still partially doing it because they want to support the tournament but a much, much bigger part is that they get something out of it that lets them enjoy the tournament more. It's not just that they're getting something out of it, it's that it's keeping them involved in that specific event. To throw out some numbers, if with kickstarter it's 90% donation with this it's more like 50%. If you're putting stetch goals on the amount added to the prize pool (say, at $500 added some kind of round robin is added to the tournament or fly some high profile player out) that number will change. Either way though, because it's a low price point and their value in is closer to their direct value out (meaning not including the tournament itself happening) it's easier to get people to open their wallets who wouldn't have before.

I should also mention that Kickstarters are more stressful for people since it feels like letting people down if they don't donate as opposed to dota2 feeling like paying for fun extras. This exacerbates the divide between the two with kickstarters up-selling people who would have already bought and dota2 bringing in people who otherwise would not have.

The two are different systems that get different, to use a phrase from when I was doing quant marketing, client signatures. Saying put your money where your mouth is doesn't really address the questions of what are they getting for that money (the tournament customization part of the dota2 approach lets you cast a wider net because as long as one of the options is what someone wants they've got a reason to give), how much is that worth to them, does giving that money generate further engagement with the event itself which will make them more likely to give in the future, and how does giving that money make them feel.