We're kinda big on Splunk, everything that remotely looks like log data get shipped of to Splunk.

I've worked with ELK before and I'm not a fan, the usability is very low compared to Splunk. It's much cheaper though. At a previous employer we switch from Splunk to ELK and the number of searches we did on a daily basis dropped to almost zero. Before that almost every support "ticket" would start with a Splunk search.

You could also try out https://www.humio.com. I only seen it deploy by one customer, but it looks nice.