Check when they last did a year end in AP. If they don't do them there could be a lot of transactions still in the "current" table. I believe those two reports scan through all of that to generate the Open Payables and the pre-check registers.

Also, when considering the speed of generating reports or accessing information in Adagio, the amount of RAM and especially the disk speed of the server are very important. Things may look faster if you're pulling data down to a local machine because it may have a faster (SSD) hard drive compared to the server as well as no network lag.