Well, I do need to qualify that. In a general cost-basis sense, it may not be worth it. Why?
The Comparison Basis Costs
First, let's focus on the solar function alone and let's reference a model type that is available with or without solar. The DW-6900 (non-solar) MSRP is $99, and the GW-6900 (solar/atomic) MSRP is $130. That's a $31 difference, and probably a reliable amount when considering both models at discounted prices.
The other price consideration is the battery. If you're resourceful enough, you can buy yourself a quality name CR-2016 replacement battery for $2 shipped. A CTL-1616 rechargeable battery is usually available for about $15 shipped from most sources, but if you're resourceful enough you can pick up one for $10 shipped. These are prices based in the USA, and of course the prices will fluctuate quite a bit for other countries.
Frequency of Battery Changes
Now, CASIO rates the DW-6900 as lasting for 2 years on a single battery. We've seen plenty of testimonies of standard G-Shock watches lasting much longer than that, even as much as 8-10 years. But let's pick a middle-ground number, where the battery needs to be replaced every 4 years. CASIO neglects to tell you what the solar rechargeable battery lifetime is, because the thought of replacing it is really the "antithesis" of their whole solar watch marketing campaign ("never needs batteries"). But realistically speaking, the CTL-1616 battery will not likely last more than 15-20 years. But let's be a little generous on this and say it lasts 24 years.
So, given the assumed details I've set up, it's time to do some generalized calculations.
The DW-6900 incurs a $2 battery cost every 4 years, adding up to $6 every 12 years, assuming of course that battery prices remain the same.
DW-6900, year 1: $99. Year 12: $105 (+$6 for batteries). Year 24: $111 (+$6). Year 48: $123 (+$12).
GW-6900, year 1: $130. Year 12: $130 (+$0 for batteries). Year 24: $140 (+$10). Year 48: $150 (+$10).
Let's look at the cost difference at the end of 48 years: $27. So, the cost difference reduced by $4 over 48 years. I have to say, good luck about ever living to see your total watch cost ever "breaking even"! If we "played by the rules" and changed the DW-6900 battery every 2 years, you would have to go 52 years before crossing over the "break even" point.
Of course, in this case I've assumed you're prepared to change your own watch battery. If not, I think the usual "discount" service cost is about $10-$15 at your local watch jeweler/technician. If you have to pay this each time, then... well, the solar option starts looking a bit more promising!
--> Battery + Service charge = $10, or $20
DW-6900, year 1: $99. Year 12: $139 (+$40 for batteries). Year 24: $179 (+$40). Year 48: $259 (+$80).
GW-6900, year 1: $130. Year 12: $130 (+$0 for batteries). Year 24: $150 (+$20). Year 48: $170 (+$20).
Difference: -$89, making it more cost effective going with solar.
Conclusion on Solar
So in short, the solar feature doesn't realistically save you any money if you're prepared to change your own watch battery. If you pay to have your battery changed, then it is definitely worthwhile, if you get at least 12 years out of the battery. The solar feature does seem to be required for having the atomic function (purportedly to compensate for the heavy drain on the battery). So if you want atomic, you do need to have solar (at least the way CASIO plays it out).
The only caveat here that I can think of, is that in some cases you may not be able to change your watch battery every 4 years. What if you have a requirement to go for at least 12 years without a battery change, due to your lifestyle or job requirements? Then there's the Frogman. It is suggested that the battery be changed by a certified technician to ensure complete water-tightness. If you change the battery every 4 years, the cost involved could be quite high, whereas you'd save a lot on battery change costs going with a solar/atomic Frogman model.
Now for the next question: Do you need atomic sync?
CASIO watches are generally rated at +/- 15 sec/mo. I've heard of some people reporting that their brand new G-Shock was drifting by +20 sec/mo, and I personally have bought a number of used ones that have gained anywhere from +15 to +60 sec/mo. Yet, I've also seen some people report that their G-Shock gains no more than +1 sec/mo. With atomic sync, you don't have to worry about accuracy as long as you get a consistent signal every few nights. I must point out that I've witnessed atomic watches being inherently prone to greater accuracy drift when not synchronizing nightly, compared to a non-atomic G-Shock. Why? Maybe there's a secondary time adjustment step that is skipped at the factory, because it's assumed that the atomic sync feature will be good enough to compensate. And realistically speaking, if you frequently get a good signal it certainly will compensate.
Well, if you're enterprising enough, you can time adjust your G-Shock watch to correct any accuracy drift that is outside your personal tolerance (although you really need to know what you're doing in order to do it safely). If you get lucky, you can get your watch to be within +/-1 sec/mo accurate. That's probably good enough so that you can wait until DST changes for the time to manually synchronize your watch. Or, if you're more a little more obsessive about accuracy, that could entail manually adjusting your watch only once per month, using the atomic clock time display on-line. Certainly, spending one minute per month to do this isn't much at all of an inconvenience and makes having atomic sync superfluous.
Conclusion on Atomic
Basically I'd have to say that if you're motivated and skilled enough to time adjust your own G-Shock, the atomic sync feature is probably not worth getting. That is, if the non-solar/atomic version of the watch you're interested in has all of the features you want, and of course has enough aesthetic appeal for you. Some models seem to have greater visual appeal or added features to them when you spend more for solar/atomic, which of course helps entice the purchase.
Well, I think the horse has been thoroughly beaten to death. Yes, non-solar/atomic is more cost effective to buy, but... one has to remember that you should be happy with the watch you want to put on your wrist. If CASIO is clever enough to make the solar/atomic version much more attractive to you, then you should probably get it. Also, I do have optimism that CASIO will continue to improve the solar recharging capability, enough so that in time the R&D costs will have been long paid off and the cost difference reduced to where it takes less than 20 years to break even. I believe that buying their solar/atomic watches helps demonstrate interest from the customer base, and fuel the R&D for further improvements.