Hey there, Abhishek1025!
As @DelroyMonjo already mentioned, you won't have any problem with the HDDs working side by side.
You just need to plug them in the SATA ports and you will have 2 separate working HDDs!
They wouldn't work if you were to set up a RAID configuration with them, because they are different drives/capacities - thus incompatible to work together in an array. However, this is not the case with you.
As for the selection of the SATA mode - I guess you should keep it on AHCI. IDE/AHCI modes are just different ways for the OS drivers to communicate with the SATA chipset.
All drives attached to the same SATA controller will normally have to run in the same mode. If your mobo has more than 1 SATA controller, the SATA ports should have different colours. So just in case your older drive has trouble communicating in AHCI mode, you can simply change the ports and set it to IDE. I don't think this will be an issue, since you've already got it set to AHCI and haven't encountered any problem.
Hope this helped.
SuperSoph_WD