I can't say which option would be safer!
I lived in the USA at one point and the UPS Stores are what Americans would use when they needed a mailing address, like perhaps if they were sent overseas or just wanted a separate address for business or eBay matters. However, the places like you link to above are definitely aimed at a more international clientele, which may have some advantages....although my slight suspicion is that somehow they overcharge non-Americans in some way, but I could just be a naturally suspicious person!
The UPS stores use UPS for shipping, which I have found to be relaible and reslly faultless.
Using the UPS store is more like using someone you know personally. They will do all kinds of extra things, like make phone calls, give advice about other services you may need, let you store items at their place, pack and unpack things, tell you how to do other things in the USA, basically anything that sounds reasonable. You get to know the people there, often just a staff of 2 or 3 family members. I think the other places you have in mind are very strictly for forwarding things, while UPS Store does many more services....also the links above seem like they are more formal about what you can ask them to do..... if that is precisely all you ever want, maybe they are best.
UPS stores in smaller cities are cheaper, but are also more likely to ask what the hell a European needs an American address for...eBay needs are very common though. People in the midwest and south are friendlier!
Do check rates....your original options may be the best priced, and they already have in mind what you need and know how to price it, at a UPS Store you will have to explain more about what you need... but for me the personal service and greater flexibility are worth having to explain to someone who doesn't have many European customers.
try this one