Those terms are not terribly meaningful in the choice of internet service. What's important is traffic policies, oversubscription policies, peers, etc, all of which are more or less irrelevant to the underlying networking technology used. None of the important info is typically available to a consumer buying an internet connection.
Presumably the newer system has advantages, but they might just be cost structure for the provider. Newer stuff is typically faster, but then again, as people migrate, the older system may become faster due to lower utilization.

Very hard to say, and ATM vs. Frame Relay in itself isn't enough info to really make a meaningful claim. If you're happy with what you have... If you're willing to gamble a few bucks with the odds mostly on your side...