Level titles are easier to remember. If you reference Taxing 6, I have absolutely no idea what level that is unless I go look it up. If you ask me about Compression Method 1, however, I know exactly what level you're talking about. The level titles are also probably less likely to change than rank and position. While individual levels may potentially get renamed, as one develops a pack, it's quite likely that levels can and will be re-ordered based on player feedback about the difficulty - and moving levels around can alter the positions of several levels other than the one that was directly moved.
The replays have the level titles stored in them, but if you aren't quite sure which replay corresponds with which level, opening a bunch of replays in a text editor until you find the one you're looking for is a pain. It's particularly bad with the contest packs, because then when people submit replay packs that haven't been manually renamed, you can't just open your level in the editor and bring up the replay associated with yours. Instead, you have to either open replays until you find the one that matches your level, or you have to go open up the contest pack so you can check which position your level got inserted into.
If I have to choose one, level titles are more useful, in my opinion. But probably the best would be an order of pack->rank->position->title->timestamp etc. The filename is what you see when you're selecting a replay, after all. The pack information, in my opinion, is mostly only useful when working with the pack as a whole. Probably the only time I really want the position information is if I'm going through the pack of replays sequentially. When I'm working with individual levels, whether or not those levels are part of a pack, the title is a lot more helpful for finding the replay I want.