Is the R9 290x worth it over the gtx 970 for 1080p ?

The 'issue' of the GTX970 memory is down to its internal design and how Nvidia cut it down-the GTX970 is a cut down GTX980-it's been common practice to do this for quite some years BTW.
Essentially the GTX970 DOES have a full 4Gb of memory but it's divided into two chunks; a fast 3.5Gb and a slower .5Gb, some have said they get stuttering issues when the card is fully loaded and it has to use that slower .5Gb, I never had any problems for the short time I had a GTX970, though-plenty of other problems but no stuttering.

The performance points are just down to the age of each part, the GTX970 uses a new design, the R9 290X is, by computer standards, old.

Either can max out even hardcore FPS games on a single 1080 display and are actually overkill for 99.9% of PC games, you'll only cause either of them any real problems by adding insane amounts of anti aliasing.

R9 290X: Get it because; It's cheaper and is better at higher resolutions, Mantle (an AMD developed software similar to DirectX but faster) can improve performance in games written to use it . Leave it because; It uses more power and creates far more heat, which means it needs a big cooler to keep it cool without making excessive noise, and good case ventilation, probably the best available is the Sapphire Tri-X, mine's no noisier than a couple of quiet case fans but it also 12" (30cm) long!

GTX970: Get it because; PhysX (handy but not widely adopted), DSR (gives the impression of a higher resolution at the cost of some performance), oodles of AA options, proper adaptive Vsync, Shadowplay (less performance hit when recording gameplay than Raptr, which AMD uses), lower power consumption, less heat and, generally, less noise and possibly better DX12 support than the R9 290X. Leave it because; Cost, still some issues with coil whine (a sometimes loud squealing/buzzing when under load), can be fussy about what power supply it's hooked up to (mainly older units), Some like the Geforce Experience software, I find it intrusive.

Ignore; Driver issues, both offer stable drivers, those reporting issues are usually causing those issues by installing non certified mods off the net or not keeping their systems/games updated. Fanboys telling you the R9 290X is hot and noisy, with a half decent cooler it isn't. Fanboys telling you the GTX970 suffers horribly with coil while (some do but you can return it under warranty) or the memory issue exists (it doesn't).