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Hi: It depends on what the DGP of the original process is. Is the process trend stationary or difference stationary ? If it's trend stationary then de-trending is the way to go. If it's difference stationary, then differencing is the way to go. The two models are quite different: Trend Stationary: $y_t = \beta_{0} + \beta_1 \times t + \epsilon_t$ ...
Let me try to write formulae to explain the differences: When $X_t=a+b\,t + c\,\xi_t$, where $\xi_t$ is an iid centered and reduced noise (ie $\mathbb{E}\xi=0$ and $\mathbb{E}\xi^2=1$. With $X_(t+1)-X_t=b + c\Delta\xi$, you read that you increased the amplitude of the noise $\xi$ by a factor $\sqrt{2}$, you removed $a$ and you have no more time dependent. ...