Does friction decrease as objects move faster against each other?
Friction is not a fundamental force itself, rather it is a macroscopic collective effect of the interactions between atoms and molecules of the two surfaces, dominantly electromagnetic interactions. Yet in reality, it can depend on a large number of other factors such as the relative speeds of two surfaces, the way the atoms or molecules are arranged in the two solids, and so on. The coefficients of static and kinetic friction pretty much summarize this unimaginably complex interactions for most common materials, and we use those coefficients to simplify our calculations without taking into account all the complex interactions. And there surely is a bound within which these coefficients can really yield satisfactory results. Outside the applicable conditions, they are mere nonsense. So those coefficients can not be taken too seriously, they do not correspond to a fundamental law of nature, rather they summarize the results of a large number of experiments for the purpose of making our calculations easier.
The friction force increases with increasing velocities, until you start to produce a lubricating layer of fluid by melting the surface. The variation is slow, but noticible, and the effect is most noticible at the start.
Notice that this is the opposite behavior of static friction, which happens only at zero velocity. The most likely reason for static friction is explained here: Why are there both Static and Kinetic Friction?
The experimental data I base the answer on is this paper which is very nice.
Friction is quite a complex problem, and velocity-independent dynamic friction
$$F_\text{df} \ne f(v)$$
is an approximation. In general dynamic friction could increase or decrease with larger velocities, I don't think there is a rule of thumb. However, it is changing continuously and change is rather small.
However, there is a real difference between static friction
$$F_\text{sf} \le \mu_\text{sf} N$$
and dynamic friction
$$F_\text{df} = \mu_\text{df} N$$
in sense that maximum static friction is generally larger than dynamic friction
$$\mu_\text{sf} N = F_\text{sf,max} > F_\text{df} = \mu_\text{df} N,$$
$$\mu_\text{sf} > \mu_\text{df}.$$
Between static and dynamic friction there is a really sudden drop of friction force as body starts moving and this is real, not an approximation. This fact is used by ABS antilock breaking systems, but that is whole another story.