I have been thinking about this from the technical performance of the glass and container itself, and on balance think rims up for domestic, and rims down for catering, but it is not black and white as different glasses have different performance and durability characteristics (and are designed for different use). To answer this fully need a huge amount of writing, - which I will avoid, so apologies if my assessment below is limited.
1. There is usually a chemical and design difference between domestic glassware and catering / food service glassware
2. There are different types of finish to the rim.
3. There are chemically different types of domestic and catering glass.
Catering / food service glasses will often either contain more alumina than domestic glasses, making them harder and more scratch resistant / dishwasher durable. Scratches are the enemy of glass durability (assuming it has been tempered or annealed correctly). Some catering glasses, especially pint pots (by law) are also toughened, which makes them 4 to 6 times more resistant to failure. Catering glasses are also designed / shaped to be more resistant to failure, so the comparison of whether catering and domestic glasses should be stored rim up or down is actually not really relevant - not generally comparing like with like. Catering glasses are also designed for different use and environment, hence often thicker in section etc.
Rims - typically there are 2 types of rim, 'beaded', where the rim is effectively 'melted' to polish it, and 'cracked off', when the rim is basically, scratched and broken off before polishing on a wheel, (posher glass). Cracked off is more vulnerable to chipping and should always be stored rim up. Beaded (if done right) will be tougher, but is still no comparison to the strength of the base, so I would again still store rim up. If heat treated badly then storing down could result in annealing failure, where the whole rim could become detached from the rest of the glass, though this is just as likely to occur during washing etc.
Types of glass - You get soda glass, which is your general glass, crystal, which contains lead, or barium, and borosilicate, which is your 'chemistry' glass. Borosilicate is chemically the strongest and most resistant (of these 3 glasses), but rarely used in domestic bar-ware etc. crystal is very soft, easy to chip, easy to chemically attack (bloom) and usually has cracked off / polished rims. therefore crystal MUST always be stored rims up (and never dishwashed). Soda is your general glass. Basically soda is added to the silicon network to soften the glass, making it easier to work, and lowering its melting point, reducing production costs. Cheaper soda is beaded on the rim, and has more soda added to further reduce costs, but makes the glass less durable, (catering soda has alumina added to strengthen it). Thus technically some soda glasses will be fine to store on rims and others wont. therefore unless an expert, or not caring, I would store domestic soda glasses rims up. Catering is often stored rims down as, they are designed for it, are stronger and it allows them to dry and stay clean in a commercial and dirty environment.
As a by, the dishwasher can be used as a 'quality test'. Domestic glasses should never be washed in a dishwasher as the alkaline nature of the washer attacks and etches the surface of the glass over time. The speed of this clouding of 'blooming' of the glass can be used to determine the relative soda content of the glass, and hence quality of material. The higher alumina content of catering wear protects against this.