One does not compare the absolute values of two AICs (which can be like $\sim 100$ but also $\sim 1000000$), but considers their difference:
$$\Delta_i=AIC_i-AIC_{\rm min},$$
where $AIC_i$ is the AIC of the $i$-th model, and $AIC_{\rm min}$ is the lowest AIC one obtains among the set of models examined (i.e., the prefered model). The rule of thumb, outlined e.g. in Burnham & Anderson 2004, is:
- if $\Delta_i<2$, then there is substantial support for the $i$-th model (or the evidence against it is worth only a bare mention), and the proposition that it is a proper description is highly probable;
- if $2<\Delta_i<4$, then there is strong support for the $i$-th model;
- if $4<\Delta_i<7$, then there is considerably less support for the $i$-th model;
- models with $\Delta_i>10$ have essentially no support.
Now, regarding the 0.7% mentioned in the question, consider two situations:
- $AIC_1=AIC_{\rm min}=100$ and $AIC_2$ is bigger by 0.7%: $AIC_2=100.7$. Then $\Delta_2=0.7<2$ so there is no substantial difference between the models.
- $AIC_1=AIC_{\rm min}=100000$ and $AIC_2$ is bigger by 0.7%: $AIC_2=100700$. Then $\Delta_2=700\gg 10$ so there is no support for the 2-nd model.
Hence, saying that the difference between AICs is 0.7% does not provide any information.
The AIC value contains scaling constants coming from the log-likelihood
$\mathcal{L}$, and so $\Delta_i$ are free of such constants. One
might consider $\Delta_i = AIC_i − AIC_{\rm min}$ a rescaling transformation that forces the best model to have $AIC_{\rm min} := 0$.
The formulation of AIC penalizes the use of an excessive number of parameters, hence discourages overfitting. It prefers models with fewer parameters, as long as the others do not provide a substantially better fit. AIC tries to select a model (among the examined ones) that most adequately describes reality (in the form of the data under examination). This means that in fact the model being a real description of the data is never considered. Note that AIC gives you the information which model describes the data better, it does not give any interpretation.
Personally, I would say that if you have a simple model and a complicated one that has a much lower AIC, then the simple model is not good enough. If the more complex model is really much more complicated but the $\Delta_i$ is not huge (maybe $\Delta_i<2$, maybe $\Delta_i<5$ - depends on the particular situation) I would stick to the simpler model if it's really easier to work with.
Further, you can ascribe a probability to the $i$-th model via
$$p_i=\exp\left(\frac{-\Delta_i}{2}\right),$$
which provides a relative (compared to $AIC_{\rm min}$) probability that the $i$-th models minimizes the AIC. For example, $\Delta_i=1.5$ corresponds to $p_i=0.47$ (quite high), and $\Delta_i=15$ corresponds to $p_i=0.0005$ (quite low). The first case means that there is 47% probability that the $i$-th model might in fact be a better description than the model that yielded $AIC_{\rm min}$, and in the second case this probability is only 0.05%.
Finally, regarding the formula for AIC:
$$AIC=2k-2\mathcal{L},$$
it is important to note that when two models with similar $\mathcal{L}$ are considered, the $\Delta_i$ depends solely on the number
of parameters due to the $2k$ term. Hence, when $\frac{\Delta_i}{2\Delta k} < 1$, the relative improvement is due to actual improvement of the fit, not to increasing the number of parameters only.
TL;DR
- It's a bad reason; use the difference between the absolute values of the AICs.
- The percentage says nothing.
- Not possible to answer this question due to no information on the models, data, and what does different results mean.
