Is beauty universal?
Fitness

Fitness is a trait which, when high is pretty much always attractive to potential mates in all species. However, fitness is definitely not an "aestetic characteristic".

Traits that are often correlated with fitness

There are some "aestetic characteristics" that are correlated to fitness in many species, such as body weight. Such trait are therefore often correlated with what individuals find appealing.

Body weight is a standard examples. Heavier individuals often have better competitive abilities, better foraging abilities and therefore have a higher fitness. As a consequence body weight is often used a s a proxy for fitness.

Relative body characteristics

Novel traits in a population can be evidence of parasitism and therefore would tend to be considered as non-attractive. However, counter to this intuition, it has been shown typically in birds having high sexual selection, that individuals having novel traits are more attractive.

Why is there a lack of generalization?

To build the intuition I would just say that given the gigantic phenotypic diversity that exist among all species that perform some level of mate choice, it is pretty clear that you will not find a simple morphological trait that will be attractive to all species.

Mating preferences evolves. Individuals that are attracted toward individuals that will yield to a high progeny (and low sexual conflict and low transmission of parasites) have higher fitness their preferences increase in frequency in the population. As a consequence, individuals like whatever is (should rather say 'was') favoured in the population. Now, in some population individuals are selected to be small, or to be big or any other things. This is the process of natural selection applied to mating preferences.