Before I made my choice I did extensive research and from my humble opinion I think they are pretty equal.
As with cameras and lenses I think the choice of software really depends on how you intend to use it

Alot of photoshopping or finally getting that pile of images sorted and ready to work with?
Earlier I used photoshop and thought I couldn't live without all the post processing tools available, but I was so wrong... Either one of them will most likely improve how you store, tag and manage your images.
I am not pixel peeping, and the brushes and tools provided in Aperture is good enough for me. Actually I think they are more forgiving that in PS that put all the responsibility on me...
I picked Aperture.
Four things I how come to fall in love with (that was a total surprise) and that last time I checked was not supported in LR:
- being able to instantly produce a professional looking book (the little time you need to spend compared to the result is ridiculous) If you think you will produce photo books, family year book, event book or whatever, I think this feature alone should make you go for Aperture. Apple.com has tutorials that just shows you how powerful it is.
- being able to simply create a slideshow with music, photos and video (after som practice you can produce a 5 minute media show that will make your friends and family cry of joy

Yes, note family... for professional use I dunno if it is sufficient)
- face recognition. you dont need to tag images with names on people that are in the shot. the face recognition works very well.
- tag images with GPS coordinates (or store it automatically if your camera supports it). When you have tens of thousands of images it simply brings you just another beautiful way of getting hold of those images you want. It complements tags, ratings etc very well.
As said earlier.
Watch the tutorials and perhaps try the demos. But more importantly, decide and get going. I don't think you will regret your choice whichever software you choose.