Which question should one answer?
There are two questions here. The first is “which one [sentence] is better?”. That is a question of usage, which @sumelic demonstrated can be answered by reference to sources such as Google Books. The second I think is more fundamental, and is the one I shall consider:
“Why would shave take the ending -ed when eat takes the ending -en in the past participle?”
Because in English there are strong verbs and weak verbs, which form their past tenses according to different systems. Eat is an example of a strong verb, shower is an example of a weak verb, and shave is a verb that was originally strong but has changed so that it is mainly weak, but with some strong forms surviving as less-used alternatives.
This is explained in the Wikipedia article on Germanic strong verbs:
“In the Germanic languages, a strong verb is a verb that marks its past tense by means of changes to the stem vowel (ablaut). The majority of the remaining verbs form the past tense by means of a dental suffix (e.g. -ed in English), and are known as weak verbs.”
In the example sentences we are dealing with past participles — the past participles of weak verbs in English (a Germanic language) end in -ed (or -d or -t), whereas those of strong verbs usually end in -en (or -n). However to clarify let us look at three forms of the verb: the infinitive, the simple past tense (aka preterite) and the past participle used with an auxiliary (have (’ve) in the examples). In addition I have included the participial adjective (where it occurs), which, although originally formed from the past participle, does not necessarily evolve/degenerate in concert with it in the case of strong verbs.
The table shows the standard strong form with eat (eat, ate, eaten) and the weak form with shower (shower, showered, showered), together with an additional example where there is a good example of a participial adjective, drive for a strong verb (p. adj. ‘driven’, as in “the driven snow”) and escape for a weak verb (p. adj. ‘escaped’, as in “an escaped prisoner”). In the case of the verb shave, which was originally strong, I would suggest that the strong form of the past participle (shaven) is more common today as a participial adjective. A second example, shear, is provided as both strong (shore, shorn, shorn) and weak (sheared, sheared, sheared) forms can still be found in both past tenses and the participial adjective).
As a child in an English-speaking country one encounters these older strong forms in traditional texts such as nursery rhymes, even if they have fallen out of contemporary use. The example brings to mind The House that Jack Built:
This is the priest all shaven and shorn,
That married the man all tattered and torn…
Coda: Early examples of use of past participle, shaven
As there has been some discussion about the use of shaven, I checked in the OED for early examples of its use. The entry for shave is extensive, but under the meaning 3 as a verb, “to cut off… close to the skin with or as with a razor”, there is the following:
1530 He hath shavyn away all the heare on his heed
There is a separate entry for shaven as an adjective, with the following early example of use in recognizable form:
1500–1520 Quhill preistis come in with hair shevin nekkis
(Don’t ask me about ‘Quhill’.)
Footnote: Mixed verbs
Not all mixed verbs were originally strong. Some have acquired ‘strong’ forms by analogy, as in the case of the weak verb, dive, with a simple past tense in the US of dove, but in Britain dived. (Cf. drive/drove) See the Wikipedia entry on English Irregular Verbs.