So first, you are absolutely right that both are possible but using the advantage reduces the variance and therefore speeds up the learning. I'm going to explain this with the REINFORCE algorithm.
The Policy Gradient theorem provides us with a simple formula of the gradient of a parameterized state-value function
\begin{equation}
\nabla J(\boldsymbol{\theta}) \propto \mathbb{E}_{\pi}\left[\sum_{a} q_{\pi}(S_{t}, a) \nabla_{\boldsymbol{\theta}} \pi(a|S_{t}, \boldsymbol{\theta}) \right]
\end{equation}
Where $\boldsymbol{\theta}$ is the parameter vector, $\pi(a | s, \boldsymbol{\theta})$ is the probability of the policy $\pi$ to choose action $a$ in the state $s$ while the policy is parameterized by $\boldsymbol{\theta}$.
The REINFORCE algorithm uses this proportionality and simplifies it even more, to
\begin{equation}
\nabla J(\boldsymbol{\theta}) \propto \mathbb{E}_{\pi}\left[G_{t} \nabla_{\boldsymbol{\theta}}\text{ln}(\pi(A_{t}|S_{t},\boldsymbol{\theta})) \right]
\end{equation}
which is translates exactly (just remove the $\nabla$-operator from the right and the left hand-side) to the loss function you mentioned what you mentioned:
loss = -1 * policy.logprob(action) * value
The REINFORCE algorithm can be generalized by adding a baseline which leads to: \begin{equation}
\nabla J(\boldsymbol{\theta}) \propto \mathbb{E}_{\pi}\left[(G_{t} - b(s)) \nabla_{\boldsymbol{\theta}}\text{ln}(\pi(A_{t}|S_{t},\boldsymbol{\theta})) \right]
\end{equation}
with a state-dependent baseline $b(s)$. Note that this baseline cannot be dependent on the state, otherwise the Policy Gradient theorem does not hold. Since the future rewards $G_{t}$ vary with the state, it showed that varying the baseline with the state led to better results, therefore a natural choice is the state value function $v(S_{t})$. The reason why this reduces the variance is, that the $G_{t}$ for REINFORCE and $G_{t} - b(s)$ for REINFORCE with baseline just changes the prefactor of the gradient. High gradients (removing the baseline) also leads to greedier learning but can also be more susceptible to errors. Think of it as the analogue to a (seperate) learning-rate (for each state) in classical deep learning.
Coming back to q-learning vs. advantage learning we can see this as applying the Policy Gradient theorem vs. applying the policy gradient theorem with the state value function as a baseline.
\begin{equation}
\nabla J(\boldsymbol{\theta}) \propto \mathbb{E}_{\pi}\left[\sum_{a} (q_{\pi}(S_{t}, a) \color{green}{ - v_{\pi}(S_{t})}) \nabla_{\boldsymbol{\theta}} \pi(a|S_{t}, \boldsymbol{\theta}) \right]
\end{equation}
As we know the prefactor to the gradient is the advantage:
\begin{equation}
A(s, a) = q(s, a) - v(s)
\end{equation}
TLDR:
Advantage learning is basically q-learning with a baseline, which reduces the variance and therefore speeds up learning.
