I've travelled with D4 and D600 separately. Just let me share which I think is a better option.
Given the technology these days, D4, D800, D600 produces great images just fine, even if the DR between the 3 models differ by a fair bit.
I bought the D4 with great anticipation to replace my ultra out-dated D2X, the image quality is mind-blowing + speed is horribly fast. Everything in the D4 overtook my D2X and more.
Went travelling with my D4 in less than 1 month after purchasing it.
Pros:
1. I get all the shots I want
2. I love the 16mp
3. Can use back all my CFs (over 1 TB).
4. Battery life is god-sent (I don't know how others find it, but I've fired 2000 shots on 1 single battery charge and 38% left).
5. I no longer need my SB-400 on trips. Nikkor 17-35 f/2.8 + ISO12,800 was all I needed.
Cons:
1. It's definitely more heavy than my D2X
2. Battery charger packing is a killer - dual EN-EL18 slots, vs D2X's single battery charger (I still brought 2 EN-EL18s for my trip).
3. Attention grabbing with it's mirror and shutter sound, I could almost spot the lady opposite me with a D800E look over when I fired off my D4.
4. I was doing a lot of hikes and the inability to remove the grip was painful
Images came out great, speed, lowlight shooting (ISO12,800) is wonderful. The D4 (if you have a budget) is wonderful beast and if you need the ruggedness, it is there.
Comparing with the D600
Pros:
1. Lightweight
2. 24mp is suitable for generally anything and even printing.
3. Works as good as the D4 (slightly better DR)
4. 1 32GB SD card averages me 1000+ 14bit NEF.
5. Battery charger is small and compact.
6. As with D4, ISO6,400 proved sufficient with Nikkor 17-35 f/2.8 and I no longer needed my SB-400.
7. I removed the grip for trip.
Cons:
1. Battery life in colder countries is a worry (I also brought 2 batteries but need to monitor their charge regularly).
2. SD Cards (Con for me as I had to re-purchase storage)
Evaluation:
I eventually decided I would indefinitely, use the D600 for future trips. Reason it being lighter, delivers almost the same image quality as the D4 (naked to the eyes).
For those who mentioned printing, I've done extremely big prints using D2HS and D2X, so MP is not really the issue here. It's how you PP the image before printing.
D800 at 36mp printing vs a D600 at 24mp printing, you shouldn't see much of a difference until you go super big (I really mean super big).
Do I need a D4 or D800 for travels? No. The D600 will suffice.
I've also used the D600 + 50 f/1.8D for portraits, and the results were fantastic. Mounting a Carl Zeiss 85 f1.4 proved even better results.
I'm not range completer, but I would choose the 17-35 f/2.8 for it's renowned wide angle quality (and yet f/2.8) for travels.
The Nikkor AF-S 24-70 f/2.8 would come perfect for the regular group/family shots (the 17-35 can do it too).
The best thing about this is, you can mount a LEE filter holder on both glasses (77mm) and bring them on trips.
With a 15K budget, one can either top up to 60k and get a car, or spend it on D600 + 17-35 + 24-70 + 50 f1.8.
What I recommend is based on my findings and the lenses suit my taste. Might not suit others...As for D4S, I doubt you need it.
I've done landscapes on both D4/D600 with LEE Filters, as well as portraits on both, the D600 can definitely be considered (or D610).