I have no past experience with Ubuntu. I just want to use it to see whether it is as good a Windows 7.
My config is AMD FX 6300 3.5 GHz,8GB RAM,AMD R9 270X and a 970 chipset motherboard.
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The difference is basically that 14.04 has a longer support period than 15.04 (April 2019 and January 2016 respectively). 14.04 would be a better choice if you are aiming on installing the system and not reformatting for a long period, for example on a server or with the more conservative desktop users.
On the other hand, if you are looking for slightly more modern software, or are just trying out the system, 15.04 would be a better choice.
If you download both LiveCDs, you can test them both without installing on your hardware, and see which works out better for your own uses.
Ubuntu 14.04 LTS is a Long Term Support release, meaning you will be able to run it until 2019 and still get system updates. This release is typically considered the more stable.
Ubuntu 15.04 is only supported until January 2016. This means that you will have to do a full system upgrade at that time. This release offers some more up-to-date packages, and may have better support for bleeding edge hardware.
My recommendation would be to try Ubuntu 14.04 with the live CD/USB and make sure everything works as you expect (hardware wise). If it does, then 14.04 is the better choice. If you find any hardware related problems, you could try Ubuntu 15.04.
From an end-users perspective, there is no real difference between 14.04 and 15.04.
Why? Your specs are good enough to support either fine, but you said you have no past experience.
14.04 is an LTS release - or Long Term Support. This means that for 5 years - or until April 2019 - Ubuntu will continue to provide security updates, among others.
15.04 is a regular release. This is only supported to January 2016.
For your needs, I think 14.04 is most suitable.
Your hardware is enough to run a Linux OS.
The difference between LTS and no-LTS is easy to get if you google it. Here is my advice:
If you want to run a stable OS, like do some important things, you should use LTS. And if you want to try new features, you'd like newer version more. And for your purpose I think you don't need to worry about the difference at all. Just try one and you'll find there's so much difference between Ubuntu & Windows. Enjoy!