I just went through the same dilemma a month or so ago and settled on Lightroom. Both have 30 day free trials and after editing in both for 2-3 weeks I found LR to be a bit easier for me. It's about a hundred bucks more expensive though. I suggest taking advantage of the free trial and decide based on your own experience.
crashwins, I've moved your thread down here into the Software forum. Take a look around and see some of the different threads. There are several devoted to Aperture, which I used to use until it failed me... It is a very intuitive program, especially if you're used to iPhoto, but it can do much more.
I now use Lightroom and am learning how to use Silver Efex and Color Efex.
Don't hesitate to ask any questions on any of the older threads or right here, too.
Look down towards the bottom and you'll see a couple of Aperture threads with some good info. Use the Search function for this forum and you'll find a bunch of different threads that should be helpful.
I've used both Aperture and Lightroom. I settled on Lightroom because it handled RAW files for older Canon and Nikon digicams I used. The Apple software didn't support the older file formats, so I would double check that point if I had older camera files that I want to have supported.
I recently upgraded to Lightroom 3 and use the Photomatrix Pro and Nik software plug-ins. I'm looking into getting the Topaz suite of plug-ins because they are on sale until Oct 20th.
You can download trials of both, which I highly recommend.
I wanted to go Aperture, but in the end went LR. The reasons for me were:
1) Aperture seems like a side business for Apple. LR is at the core of one of Adobe's businesses. Apple has a habit of suddenly killing off products not at it's core.
2) Aperture RAW updates always seem behind LR.
3) Lightroom is pc AND mac. Love my macs (I have about 5 in my house!), but nothing is forever. If I ever went back to PC, I can port my LR database over. There's no choice with Aperture.
That being said, the biggest differences right now are workflow: With Aperture you have an image, and can do anything with it. In Lightroom there are 5 modules, and the two most important have some tools divided between them. For instance, you cannot crop or straighten in the "Library" module. You have to go into the develop module. It's just a click, but it's a little inelegant. Some folks hate LR because of it, but all the REST of the benefits outweigh that issue, IMO.
One other side note (personal issue) -- I find the Aperture interface fonts to be too small.
Last note: From what I've seen, there are far more third party sites with tips/helps, etc. for LR than with Aperture. One you can Google for is Lightroom Killer Tips, but there are many others, too.
I went with LR3 because of the noise reduction ability from within LR and because I work primarily on a Macbook and the performance was quite a bit better. I also felt that Aperture 3 was just not quite as stable as LR was at the time. That said, I detest the LR UI and nothing would please me more than to get LR3 (and Photoshop CS5) off my computer permanently. If Apple managed to give Aperture better built-in noise reduction and make it more stable I would drop LR so fast it would make your head spin.
Aperture is only available for OSX, whilst Lightroom works on Windows and OSX. The LR license covers two instillations and both operating systems. Unless you only ever use OSX Aperture is of no use. All the other factors fall by the wayside on this one for me as I use both platforms.
I have tried both programs and liked both. However, Aperture seemed to be more buggy than Lightroom, which was still beta at that time. Looking at the past I saw that it took significantly more time until Aperture supported new cameras than Lightroom. I don't know if I will work on a Mac forever and I would loose all development informations, if I changed the system, because Aperture is available for Mac only. Thus I bought Lightroom and I am happy that I did so. However, your mileage may vary.