Graphite is "numbers only." You can't throw logs at it.
Influxdb will be more similar to ElasticSearch, in that it will accept logs and events, and let you query and generate graphs and subsets of the data.
ElasticSearch has more mature clustering/scaling, and last time I checked, much more efficient queries. I don't know if Influx is winning the polish game, but I suspect it depends on your use case.
(disclaimer: bonsai.io founder)
Graphite compliments the ELK stack and does not replace it.
Logstash is great at extracting metrics/numbers/data out of your logs. You can then use the graphite/statsd output plugin to graph that data.
Right now I'm in the process of setting up a Log aggregation/metrics system for PCI logging, and general server stats. Right now I'm using Elasticsearch, with Logstash and Kibana, and then piping OSSEC logs into Elasticsearch for security logging. I like the idea of this ELK stack, but it's not very polished imo.