Whats cheaper shipping suitcases or check in bag? when moving?

In reality, the vast majority of baggage delivery options that are available to travelers do not compete on price with registered luggage. ... "The base price of LugLess is generally cheaper than registering a bag, it is always cheaper than registering a second bag, and much cheaper if you are registering more than three bags.

not at all in my opinion

It might be a combination depending on the airline. The fees for the first two are usually relatively reasonable (i.e. cheaper than shipping) and then the prices skyrocket. But check luggage shipping places like lugless https://app.lugless.com/pricing/. I picked from random dates from Newark to Orlando for 3 bags and the fee was under $100.

You could also get a credit card from that airline and usually get 2 bags for free and the 3rd one should be at the "first" bag fee (this would probably be the cheapest, but of course you have to get that credit card, but the first year is usually free and you can cancel it if needed)

Sending suitcases via the post office is almost always less than paying for excess checked luggage. 

Depends greatly on the weight and what airline you are flying on.  Baggage fees are not the same on each airline.  Southwest, for example, gives you 2 checked bags included in your ticket price.  Your 3rd one is $75.  That would almost certainly be cheaper than shipping 3.  AA charges $25/75/150 for 1st/2nd/3rd bag.  In all cases, there will be a hefty fee ($100 for AA) for each bag which individually weighs over 50lbs.  

So you need to figure out your flight, luggage, and shipping costs all at once to find the bests deal.