My next guitar, I have decided, will be a hollowbody. I'm looking at Epiphone Dots and similar guitars, but I've heard good things about the Ibanez Artcore. Has anyone got any advice regarding the differences of these guitars?? Is it worth saving up for a Gibson? (would take me a LONG time)

And I play Alternative Rock/Punk Rock, if it helps.
It sounds like you may like the idea of a semi-hollowbody, but you have little or no experience with them. I suggest you get a cheap one (The Epi Dot Studio is a good benchmark to judge cheap semi-hollowbodies by) first to make sure you're comfortable with the different shape, feel and tone that comes with archtops.

As far as the Dot goes:

Stock Epiphone Dot vs 20-ish year old Gibson 335 through a pretty standard no-frills amp. It's surprising how little difference there is.

Also, Epiphone were beating Gibson in the archtop market before Gibson bought Epiphone, and they've kept that quality up throughout their ranges - the better Gibsons are of course better than the cheapest Epiphones, but really the best archtops you can get hold of are the top-end Epis.

As far as the Ibanez go, they are good guitars, but in case you can't tell by my above statements, I think the Epis are a better buy. The Artcores do have more comfortable necks for most people, but they just don't feel like a proper archtop to me. You can't really go wrong with them, they've got the quality.

Just holding back and saving for a Gibson (though again I say, the top Epi archtops are better - there is a reason why they cost more than the Gibsons in most countries y'know) isn't a good idea though.
I tried out Epi's extensively, also Artcores. I bought the AS73. Better neck playability, better quality and appearence, but the Dots do have slightly hotter pickups.