Depends on three things for me. Distance, size, and if I'm financing.
If it's in the Houston area and doesn't require a lowboy, I've got a solid guy I use.
If it's larger or unique, that usually means more variation in quotes. In my experience, the shippers that dealers use are usually better at this. Dealers know who's reliable for larger loads. Maybe they have the sway to force shippers to eat extra costs or the dealer absorbs some of it. I'm not sure. But it's less likely they come back to me saying "oh, this is actually gonna cost $X more".
Generally I feel more comfortable using the dealer shipping. Then there's two parties who have an incentive to use a good shipper and hold them accountable.
If I'm financing it and they can put it all on one invoice I'll usually go with their shipping for simplicity. It makes virtually no difference on my monthly payment.
Either way, if you're sourcing multiple quotes and one is significantly lower than the others, watch out. They likely either (a) don't know what they're doing or (b) will hold your shipment to cover "unexpected costs".