Just adding here my thoughts on the matter.
OAI-PMH is an excellent protocol for exchanging persistently uniquely identified digital objects. It allows external systems to keep track of changes (because records are uniquely identified), get only the delta ('from' parameter), it is server-side performant (in the sense that it allows one paginate through the results) and so on.
However, when it comes to usage statistics, trying to embed such data inside the OAI-PMH protocol, which was not created for the purpose, will result in subsequent hacks to keep 3rd party systems correctly synchronised/consistent. Due to the nature of the data, usage statistics is not a good example to apply OAI-PMH. The simple fact that there is no need to have uniquely identified events (might really be overkilling) makes almost all the OAI-PMH arguments fell.
So, in my point of view, COUNTER + SUSHI fits the purpose a lot better.