Hi Asim,

Generally a download accelerator increase the speed of downloads by collecting from the fast servers or by splitting them or else.
Whatever technique they may use, what we care is the speed, right ?

IDM and DAP are the 2 most popular download accelerators on the web. So, when comparing them the most influencing factor is the speed they provide.

IDM: It is a tool to increase download speeds by up to 5 times, resume and schedule downloads. Comprehensive error recovery and resume capability will restart broken or interrupted downloads due to lost connections, network problems, computer shutdowns, or unexpected power outages.
Simple graphic user interface makes IDM user friendly and easy to use.Internet Download Manager has a smart download logic accelerator that features intelligent dynamic file segmentation and safe multipart downloading technology to accelerate your downloads.
Unlike other download managers and accelerators Internet Download Manager segments downloaded files dynamically during download process and reuses available connections without additional connect and login stages to achieve best acceleration performance.

DAP: It is the world's most popular download manager brings much more to the table than fast file transfers, but it definitely delivers those, too. Increased download speeds are Download Accelerator Plus's bread and butter, speeding up downloads by almost 200 percent in most cases and occasionally as high as 400 percent.
Besides splitting files into smaller pieces, it thrives on automatically seeking faster mirrors. It also can get a file simultaneously from several sites, which is useful if a particular site limits the download speed; it can resume downloads; and it can preview some media files while downloading.

Here is a quick pros and cons about both of them:

DAP Pros:

• Light wight and Fast
• Accelerate videos and can download YouTube videos in a single click.
• User friendly and simple Interface.
• Free to use.

DAP Cons:

• Speed varies everytime, You can’t always get a constant speed.
• Can only download flvvideos from YouTube.
• Can’t always withstand slight disconnections, easily errors while downloading.

IDMPros:

• Increases the speed upto 5 times. The Speed is accelerated and maintains at a similar level throughout..
• Can pause and resume downloads, It’s a great feature if you want to download large files.
• Can withstand and resume broken and interrupted downloads. 
• Can download flv,mp4 videos from Youtube and also from other sites
• Can schedule downloads.
• Other features like ZIP preview.

IDM Cons:

• It is NOT Free. You have to pay after the trial season is over.

IDM is the best choice for you if your willing to get the best and spent some money. But, If you don’t want to spent anything, DAP is best for you. It may won’t let you to schedule or resume downloads but can give you an amazing speed.I hope this helps in choosing the right software for your PC.

Regards,
Lokesh