If by "trend," you mean change or continuity in the level of the variable, then traditional regression is not terribly helpful, as it takes no account of means.

The most common contemporary techniques (at least for continuous data) are various forms of change modeling that distinguish between the sample-level trend and individual-level deviation from that trend -- e.g., latent trajectory models, whether polynomial, exponential, other parametric, or nonparametric; change-score models, etc.

Pat

The famous quote from George Box says: "All models are wrong, but some are useful". Sometimes a simple analysis like a T-test or a linear regression is inadequate to model a certain complicated process or hypothesis. Other times, more complicated methods are used outside the appropriate context and they yield bad results due to over-fitting or other problems.

People like to find absolute truths. When it comes to statistics and modeling, I think people want hard and fast rules. They want to say "nonparametric tests are always better than parametric tests" or "Bayesian methods are always better than frequentist". To that end, I think people want to believe that statistics is a purely mathematical pursuit that will eventually pick the winners and losers from among all the different models and philosophies within statistics using some tidy, elegant proof.

Unfortunately, the world doesn't work that way. Statistics is about more than just mathematics. When you choose a statistical model, you need to consider the distribution of the data, the potential sources of variation, the relationships among the different variables, the scientifically relevant null and alternative hypotheses, ... In some experiments, you might find several different models that all converge on the same truth. Even worse, you might find two equally valid methods that contradict one another and any choice you make between the two results might be totally subjective. While I believe that statistics should be considered a science, there is often a little bit of art to it as well.

So, when you ask if any method is "sufficient", the correct answer will always be "it depends on the data".