I have connected in Eastern USA many (prob 40/50?) times, and only missed one connecting flight, and that was a couple of weeks after 9/11, and the US hubs were in understandable dissaray.
It is certainly cheaper than going direct, in most cases, and can make a big difference in total cost when travelling with a large family or group of friends.
Inbound, no problems, your bags are checked through to UK, and you only have to travel from one gate to another. Outbound you have to queue at immigration at the US hub, this can take 10 minutes or 90 depending on which hub, amount of staff on duty, amount of international flights arriving at the same time etc. You then collect your bags from the carousel, go through US customs and hand in one form (normally no or little wait). You do not have to go to check in, just drop your bags at a transfer drop off point, normally right outside customs, and then go back through security to the gate for your US domestic flight. When you arrive at Las Vegas, you are a domestic customer, so just collect your bag and go and lose some money!
So, if cost is not an issue, yes, it is better to go direct. But don`t be put off by some of the stories about what can go wrong, in my experience it hardly ever does, and I have saved 10s of thousands of pounds over the years with 6 of us regularly travelling together.
Good luck, Vegas is certainly an interesting place.