Definitely don't give up the company relocation until you've gone through the whole package. I'm in the middle of a Navy retirement / relocation move now, and I'll tell you that the company will probably take better care of you than the Navy will.
Yes, the Navy will pack your goods and move them anywhere in the continental US, but that's about it. You'll get the mileage and lodging for the trip back after you file your travel claim, but we all know where retirees fall in the stack... We're on the bottom. If they're offering you a "full" relocation plan it could include all of your travel expenses up front, some of which are taxable and some not. I won't get into that part here, but it's a good chuck of change. You might be able to do a pick and choose thing with your relocation plan, like use your move from the Navy but still get the other bennies they offer. Can't hurt to ask.
If you're a homeowner, it could get even sweeter. Several of the relocation plans offer home selling and buying assistance, including covering title fees, attorney fees, and some other stuff. If you're a renter it might not be as sweet, but still a good deal. Plus, with a company sponsored relocation the moving company is going to have the company leaning on them to get you moved in a rapid manner. A retiree relocation... think "space a" on a MAC flight.
Here's what I did, don't know how it'll all work out yet but I'll let you know when it's all done:
I was a renter when I retired and took the company relocation plan. On very short notice (about 1 week) they moved me from VA to MS. I don't have my household goods yet, but that's only because the furniture left my house in VA on Friday and was ready to deliver in MS on Monday. I was still trying to get me, my wife, and two stupid cats down here. If I had made the trip as fast as the movers I would have had my furniture back in my new house in about 72 hours. Unfortunately I have to wait until Friday (7 days). Plus with a good relo package you get money upfront, which is a good thing. Becoming a resident of a new state when you're not active duty is pretty expensive... It cost me $650 today just to get plates for my 2 cars, and neither of them is really nice (Ford Escape and Focus). I had money saved for this kind of stuff, but it's nice to be reimbursed beforehand.
My devious plan is to rent until I qualify SRO then buy. My pay will be higher, plus I'll know the area. Then I'll use my Navy move to go from my apartment here to my new house. Plus I won't have to worry about maintaining a home while qualifying. At TAP they say you have 12 months to use it, but they also said you can extend that to 36 months. If they were lying... oh well, too late now.
As far as the health insurance goes I really don't know. I plan on sticking with the Tricare Prime stuff since that's what my kids in TN use and it's working well for them. I don't want to do anything to upset that, since it is working. I've heard about companies offering financial incentives for not using their insurance, but I've also recently (in the last 2 years) heard about some possible legislation to prevent companies from offering financial incentives to vets who use their veteran's medical benefits instead of paying for them again. I'm really not sure what happened with that, but it could be something that comes with all of this new healthcare legislation that's forthcoming.
Keep in mind that if you use the company health plan in any way whatsoever that Tricare automatically becomes the secondary to that. I tried to use set it up as a supplemental thing, but it's forbidden by law.
Also remember that sign on bonuses (and bonuses in general) are taxed at a higher rate than you salary would be. You'd make out much better with just a small salary increase than you would with a bonus. It's taxed lower, and it counts as income so you can put more into your company's 401k.
In short, don't reject the relocation out of hand... it's worth more than it might seem! Plus having your relocation people paid by the company you're going to work for could make things go a little more smoothly. My move was relatively effortless, other than the 16 hour drive with a wife and pets!
Guess I've rambled enough, plus I'm sure my neighbor is getting tired of me using his unsecured wi-fi. Good luck with your negotiations, let me know if you have any questions.
Jay