Last summer, we moved from Michigan to Georgia and we decided to rent first. The primary reason was that we had never lived in Georgia before and wanted more time to figure out where we might want to but a house. While we had come down here twice for very short trips to scope out different towns, we didn't want to rush into buying a house and later find out that the area wasn't really where we wanted to live for a long time (due to things like traffic to work, schools, overall feel of the town, the city spreading outwards and inevitably making it less rural than we'd like, etc).
Also, we didn't want to feel rushed into finding a house to buy and potentially having to settle for something we didn't really want since we were on a time crunch (and didn't have a whole lot of time in the area to really look for houses). That's the issue we've fallen into with the past couple of out of state moves we've done where we've had limited time in the area to look for a house to rent and ended up settling (either in an area we weren't thrilled with or a house that we weren't really thrilled with) due to being on a time crunch. I'd rather do that with a rental house that we only have to stay in for a year than with a house I'm buying and potentially staying at for decades though.
Another consideration for us was that it's costly to make a cross country move and by waiting to buy a house, it gives us time to build our savings back up and have a better cushion for when we do buy. We'll have a VA loan so we won't need a down payment, but there are still closing costs, costs for another move (though much less costly in-state), and incidentals should we need (new paint/carpet/appliances, etc), as well as things we might want to personalize a house we buy (new drapes, furniture, etc).
Another reason relating to cost that I'm glad we waited to buy a house is it meant we had more in savings to cover the higher than expected costs of getting established in a new state. We weren't expecting to pay $1500 to get GA titles for our vehicles (no other state we've lived in has had that high of a cost), in addition to the costs for registration, emissions testing, and driver's licenses. We also needed more hot weather clothes as I quickly realized that the jeans and hoodies I wore virtually year round in Michigan were not going to work down here. There were some other incidental costs from the move that we weren't expecting as well (having to buy a new dresser since one fell apart in the moving truck, a washing machine that stopped working shortly after we got here, needing to buy a push mower since we hadn't realized in the one time we'd seen this house before moving that there was no way to get the riding mower into the back yard...)
Overall, there are just usually incidental costs that you don't realize or have no way of knowing about when you make a long distance move so it's good to have an extra buffer built into your budget. For us, that would have been harder, if not impossible, if we dropped a large chunk of money on buying a house. Also, as mentioned before, it was important for us to know that when we buy a house, it's the house we really want in an area we will be happy for many years.