Found better technique just before publishing old, but still good technique – can the old one still be published?

Publish T1. Later, when you have time to write a whole new paper, publish T2. Doing a comparative study between the two sounds like an excellent follow-up decision as well. I'm not sure why you classify T1 as a failure... it sounds like both work and one works better.

That said, yes, it is okay to publish "failure papers." Depending on the field it might be harder to get it approved by a journal because it's less sexy to find a negative result than to find a result. This causes a measurable bias in some fields and depending on the field can be a major problem, because failed research is just as important as successful research epistemically speaking.

I am assuming you frame the second paper as describing a rejected (failed) hypothesis, because your theoretically informed expectation (=hypothesis) was that T2 shouldn't perform as well as it did.

Negative findings (rejected hypothesis) can be as interesting and publication-worthy as positive findings (confirmed hypothesis). What matters is how strong the underlying theory/model is and whether your research is designed in a way that a negative finding is a good test for a theory/model and not just straw moving in the wind. If the rejected hypothesis is strong and the research casts doubt on a model/theory that is generally believed to be true, than this negative finding is much more important than the umpteenth corroboration.

Even better if your research design aids in explaining where exactly the model/theory fails. And yet more publication-worthy if T2 not only challenges a mainstream theory/model but also performs better than a more standard technique.

Pragmatically I agree with the strategy to publish T1 first, and then T2 after spending some time exploring why T2 performs as it does. To increase chances of acceptance, stress how the 'negative' finding challenges conventional wisdom and emphasize the unexpected and strong performance of T2.