Yup, "Synths, sweeps, atmospheric type sounds" is a fairly broad category of that many synths could qualify for.
 
The best plan is to first learn what you have already that can do much of that, and then decide what you cannot do with that.  Then you will have a good reason to spend money on something else.
 
I think that the factory preset libraries sometimes don't present a synth's capabilities in the best way.  They are provided to market the synth, and often are geared towards the intended target audience.  A lot of the new synths seem to target the EDM producer crowd.
 
So sometimes it may be best to learn how to kick the tires yourself, and take it for a spin by tweaking the presets yourself.  Add some effects, layer some different sounds together, etc. 
 
Plus there is a big pile of free instruments that you can explore before laying out some cash.  Check out this post for a list:  http://forum.cakewalk.com/FindPost/3542942
 
Then there is always Omnisphere.  That is the king of atmospheric, movie soundtrack quality sounds.  But it comes with a hefty price.  Has a lot of fans, though! 

Magic Russ
I always thought Rapture was a lot more atmospheric and moody than z3ta+.

Yes, but he also mentions "trance and techno" thus I threw Zeta out for that reason.  I should have mentioned Rapture.

The main thing to realize about synths is that they all mostly produce sound the same way, using various sound sources, or combinations of sources that range from virtual analog oscillators (sine, saw, triangle, pulse, etc), wavetables, FM, modeled instruments, sampled instruments, etc. 
 
So results can vary based on the sound sources used, and how they get processed.
 
What you are hopefully buying when you pay for a commercial synth is an easier workflow to make the type of sounds that you want, as well as an inspiring factory library (presets) designed by professional sound designers that you can explore and maybe tweak.  Or if you are inclined to do so, roll your own sounds.
 
Spending time with the bundled synths, some free synths, and a few demos should give you a good idea of where to head next.

Thank you for the advice. I'll focus on what I have for now, and learn the software. Then I'll try out a few full-version demos of some synths, to see what I might be missing. Thanks for the free instrument thread, too.

I will just add that my favorite 3rd party synth at the moment is SynthMaster 2.8 from KV331 Audio.  The factory version comes for a very affordable list price of $99 with 1250 presets.  http://www.synthmaster.com/
 
Demos available, as well as a Player version with the 1250 presets for $29, or Player "Free" with 300 presets.  I bought the Player and received a discount code for the upgrade to the full version.  Plus they run occasional discount deals.  They are working on a version 3 for release next year that will be a $30 upgrade, and will include full wavetable support and other workflow improvements.
 
It ticks all the boxes, and I doubt there are many sounds it cannot make.  It covers various types of sound sources.  It is probably not the best synth to start out with, some find the UI a bit confusing at first.  The modulation scheme is probably the hardest to get a handle on.  But it is learnable if you know what an oscillator, filter, envelope, LFO, etc, are.
 
My current shopping list has several synths by u-he.  https://www.u-he.com/cms/
 
I have the u-he freebies (on my list), as well as a few demos of his best commercial synths.  I think that Diva and Zebra 2 are probably the best sounding virtual synths I have ever heard.  I have held off because they are not cheap, and I already have plenty to work with.  But one of those will probably be next.

Synthmaster is of course amazingly capable and regularly goes on sale for BF.
 
Rapture was included with CM magazine a while back.  I think you can get the back issue for $5 from Google Play or Zinio and that will give you access to the CM vault where you download all the included software.
 
Absynth would be another one to check out.  It's known for atmospheric pads.
 
If you don't play piano well, check out EZ keys.  It has an engine which adapts patterns to the chords you specify, and you can redirect the midi out to another instrument.  That's another one which usually goes on sale for Black Friday.
 
Since you have z3ta+ classic, look for the Muz3um soundset - it's dedicated to replicating the sound of older synths like Moog, Buchla, ARP, etc.
 
 

Oh yeah!  I forgot to mention the free Muz3um sound banks.  They are available for classic z3ta+, classic Rapture, and an upgraded version released for Z3TA+2 at Patch Arena. 
 
> http://patcharena.com/downloads/index.php?subcat=2&ENGINEsessID=a1b1a787409f28124f15ac8a0ff99170

And regarding Rapture classic, these are probably my favorite sounds for it.  I can get lost for hours while auditioning these sounds! 
 
Rapture Expansion Packs 1 & 2 (free for Rapture users)
https://www.cakewalk.com/...re-Expansion-Packs-1-2
 

mumpcake
...
 
Rapture was included with CM magazine a while back.  I think you can get the back issue for $5 from Google Play or Zinio and that will give you access to the CM vault where you download all the included software.
 
.... 

It was in issue 200. http://www.musicradar.com/computermusic/computer-music-special-200th-issue-february-2014-590566
 
Computer Music comes with a wide range of VSTs. Here's a list from March 2013 (more have been added, a few taken away): http://www.musicradar.com/computermusic/cm-plugins-full-list-of-our-exclusive-free-vst-au-plugin-instruments-and-effects-571808
 
Somehow I've ended up with 3 licences to Rapture (I bought it for £35 in 2009, I got it with CM200, and then I got it with Sonar Platinum)...
 
 
 
 
 
 
...the CM licence was never registered.
 
 
 
 

I'd say Omnisphere2 is the one you should go for