Basically, is there something Irish Whiskey (such as Kilbeggan) that is as good (or better) than basic Powers or Bushmills Original ?
Ok, let's start here then.
Yes, there are loads of Irish whiskeys better than White Bush or Powers. But they're also more expensive.
For me, the entry level is probably above young Cooleys generally. I'd use things like Kilbeggan for an Irish coffee perhaps. But I just find that the step up in quality from them to the likes of Powers or Black Bush is more than worth the additional few quid.
I'd rather have one bottle I like than two bottles I don't mind. So when you're talking bang for buck, the consideration isn't just buck, it's also bang. And there ain't much banging about Kilbeggan or Tullamore Dew or White Bush or Paddy for me.
For me, young Cooleys, Tullamore, etc <Paddy < White Bush < Jameson < Powers < Black Bush < Redbreast. But I suspect pot still fans (and I'm one) would more often put Powers on a par or ahead of Black Bush. I grew up on the stuff though, and it's the whiskey in my mind that all others get compared to.
After that list, we're probably heading out of the budget territory of the market.
I think given the price levels you're encountering, Powers is your best bang for buck whiskey. To be honest, if Kilbeggan was going for 15 bucks here, I'd buy a bottle for guests and for mixing into coffee or hot whiskeys too.