The quickest way to accomplish this is to avoid having to do it in the first place... Can your servers be configured to both send data to a single centralized log? I know *nix's syslog is network-aware and suspect something similar should exist for Apache and IIS, simply because companies with huge webserver farms aren't going to want to deal with each server's log individually.

If you're not able to centralize it, then duelafn's suggestion is probably going to be the quickest way to combine them. It also allows you to use tell on each filehandle before or after reading from it to monitor how far you've gotten in processing that file. Combined with checking the size of each file before starting, that should give you enough information to generate a relatively meaningful progress indicator.