How is Ubuntu 15.04 different from 14.04 in terms of installation ? As the first link says 15.04 is quite easily installed than 14.04. Why ?
The referenced statements are the opinions/experience of one person. You'd really have to ask that person to elaborate on the specific statements. That said, 15.04 is newer than 14.04 and so uses updated versions of certain elements. Some of these updates might improve your odds of getting a clean install. Some of these have been updated in 14.04 point releases, the latest of which is 14.04.3, so it's probably best to start with a 14.04 point release rather than the original (April, 2014) version of 14.04.
Remember that any given install is a bit of a gamble. For me, 14.04 (even the original 2014 release) installs fine on many computers. Hardware released since then, though, may require new drivers that aren't present in the original. Random Person X on the Internet might have problems even with older hardware and so might make a more sweeping recommendation to install the latest version.
Please do explain me about UEFI and secure boot and what do i need to with it. Why should i disable it ?
Secure Boot restricts what programs may run as boot loaders, based on cryptographic signatures embedded in the boot loaders themselves. Something that's not signed with a key whose public key exists in the firmware's database will not boot with Secure Boot active. The idea is to make it harder for malware to take over the computer before the OS has even booted. Of course, this is a good goal, but it creates an extra hurdle for Linux distributions, since the only key that's guaranteed to be present in most computers is owned by Microsoft. The good news is that Microsoft has signed many third-party binaries, including one called "Shim" that enables GRUB to boot. (GRUB then hands off control to a Linux kernel.) Ubuntu uses Shim as part of its boot process, so in theory Ubuntu should work with Secure Boot enabled.
Note that I wrote "in theory." In practice, Ubuntu usually works fine; but there are bugs (in Shim and/or in specific EFI implementations) that can cause it to fail. If you run into such a problem, you must disable Secure Boot or work around the problem in some way. Note that Secure Boot problems are almost certain to prevent GRUB from even starting. If you run into a problem later, like a blank screen once past the GRUB menu, the issue is almost certainly not a Secure Boot issue (although many people immediately think of Secure Boot and try adjusting its settings).
As a general rule, my advice is to leave Secure Boot enabled and to disable it if and only if you can't get GRUB to start.
Note also that Secure Boot is just one feature of UEFI, and an optional one at that. Many EFI (UEFI is just EFI 2.x) systems lack Secure Boot support. EFI is a replacement for BIOS. This is a critical point; many people are under the mistaken impression that EFI is just an extension to BIOS, or a minor variant on BIOS. It's not; EFI is completely different. If you know how BIOS boots, forget it all when dealing with an EFI-based system. For more background on EFI generally, I recommend you read:
Also is 15.04 good and stable enough like the 14.04 ? Beacuse I personally prefer the 14.04 due to the LTS offered.
My recommendation is to stick with 14.04 if at all possible. As noted earlier, use the latest point-release version, especially if your hardware is newer than the April 2014 release date of the original. If you have hardware problems (disks not being recognized, network not working, no sound, etc.), it may be worth trying the latest non-LTS release. At this point, that's 15.10. I do not recommend installing 15.04 at this point, since it has just a couple more months of supported life left. If you install 15.10, you should seriously consider upgrading to 16.04 once it's released; that's the next LTS version, so then you'll have support through April of 2021, should you decide to stick with one OS for so long.