I realize this is subjective and some probably like both logos. But it won't be anywhere close to the best looking ring ever if they use the current Rams head logo. Whereas if they had a really pro looking logo of a Rams head the identity would be there and you could get special building around it.
It's not like we get rings so it doesn't affect us really. Whatever they do though probably won't age well because of this fundamental problem. They will use the LA logo and everyone will be very complimentary and excited but zero chance they will end up with some greatest design ever when their logos are so weak. Just my take on it and I realize some will strongly disagree.