Personally, I have not had the horrific experiences described by many people around here with Siri, but that is pretty much the norm these days on MacRumors.
That being said, I can't see a hotel chain paying for iPhones or iPads to put in every room just for Siri. However, I am not sure how Amazon Echo supplies the security you would want or how it works without logging in with a Prime account. They would have to put together a locked down version of the Echo that is only for hotel chains, so what Echo owners experience at home could be quite a bit different than when they stay in a hotel.
As far as the Echo vs Siri debate, I don't even consider them to be in the same category. I have a couple Dots at home and they are very flexible if you setup "skills". Apple has a more secure setting and they only open it to what they can lock down on the security side of things.
Personally, I used both of the "assistants" every day. Siri is best for when you aren't near an Echo and have your phone/Apple Watch on you. Even at home, I have an Echo in the kitchen, but if I want to control bedroom lights, I use Siri. I also use Siri out by the pool to chose music to Airplay Apple Music to my stereo, and in my car, and at work for the same reasons. I use Siri more often for alarms/reminders, even at home, because it will vibrate my watch and let me know without loud alarms going off. I use the Echo for music, controlling hue lights and controlling my entertainment center (mainly turning on and off the TV).
Personally, if I had to keep just one of the services, I would keep Siri. It is on my wrist and the Echo isn't. That makes it more usable wherever I am...especially since it can control the iPhone and the Echo can't. I do think the Echo is a better fit for the hotel because it is a device that just sits there and waits for the key phrase, but its open skill set also makes it more likely to put your privacy at risk. I don't know if I would want one in my hotel room, to be honest.