My $.02 on chassidishe (or more precisely Lubavitcher) shchita.
1- We believe that learning chassidus enhances ones Yiras shomayim. So if you have someone who has yiras shomayim and learns chassidus, they are preferable to someone who has yiras shomayim but does not learn chassidus. Obviously, if the person is lacking in yiras shomayim, the fact that he opens a Tanya for 5 minutes in the morning, does not qualify him to be a shochet.
2- Separately, when it comes to shchita, the halacha is that a person should prefer a situation where he knows and trusts the shochet, to a situation where he only knows and trusts the Rov. The closest most people can get to that standard today, when the shochet is not coming to your backyard to shecht, is to give preference to someone from thier own community.
3- Regarding beards, mikvah etc... For someone from a community where those things are considered a requirement, it shows a lack of yiras shomayim to be lax in those areas. So while a lack of a beard says (little to) nothing about the yiras shomayim of a litvishe shochet, it does disqualify a Lubavitcher shochet.