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I like to sandblast and paint with two part black Epoxy primer, two or three coats works well and has the degree of flatness (semi flat appearance). Get a good sand-blaster and use 80 mesh sand or similar coal slag. Any lower mesh number will leave rust in any small pits. Get the paint on it right away because it will start to rust if you are in high humidity.
I have used powder coating and later wanted too change my trans mount on a Resto-Mod and it was a big problem to try and match the coating, never looked good. Maybe I don't the secret technique. With paint it's easy.
Some folks really like powder coating though. Stay away from high gloss black powder or paint because it magnifies small defects, factory mig weld splatter, or rust pits. Semi flat, semi gloss, or eggshell I believe is the description you are looking for. Opinions always very.
If I were going to be driving my classic vette 12 months out of the year for 10 years in rust belt states I MIGHT consider powercoating. But then I would probably dismiss that idea go with dip strip and paint.
Second choice soda blast and paint. Powdercoating is for motorcycle parts and resto-mods that are all about bling. Is your car a fair weather weekend driver? You're not doing a resto-mod are you?
I had to replace my original frame due to extensive rust on the top surface. Swung by a treatment plant in Punxsutawney, PA. Dipped the new frame in 4 or 5 tanks that cleaned, coated, treated, and cooked inside and out. It cost me ~$300! Then also epoxy primed/painted for color. We manufacture military equipment that's often used/abused in saltwater environment and treated rude. We only use epoxy coatings (my decision). My experience with powder coated farm equipment is bad. Rust migrates under PC and comes off in big flakes. Maybe it's poor prep before PC, don't know or care. I get it... PC looks great. But for durability/repairability we only use epoxy on parts that will see abuse/impacts.
I recommend paint. You probably know all this but a refresher might not hurt. Have the frame checked for straightness if your car was involved in any past accidents, check for cracks at the spring pockets and correct any welds before paint. You may also want to pretty up the frame by removing imperfections or smoothing any pitted areas. My car, the previous owner was a novice that restored the frame and failed to do these checks. That nice powder coat he had applied is history as are the urethane bushings front and rear he installed.
After you get the frame back and coated/painted, consider using air to blow out and water to flush out and remove all the garbage from inside.the frame, air alone may not do it. An inspection camera helps in this regard. Getting behind the internal baffle at the rear kick-up to clean it out is difficult. The weep drain at the rear kick-ups may need to be cleared repeatedly of small pebbles and other nasties using a small bottle brush. I had to break up countless small pebbles using a punch and hammer at the kick-up weep drain, lots of water and time and more damage to the powder coat. As Factoid suggested, If you decide to treat the inside with something like Eastwood's internal frame coating do so before mounting anything to the frame, and use a coat hanger wire to support the wand. This stuff goes everywhere so buy a roll of rope caulk from a big box store, about $6 and seal all the small holes and between all the welds top and bottom, use tape over the bigger holes and place something on the floor to minimize cleanup from any leaks. Use paint thinner/mineral spirits to clean up any that gets on the outside of the frame. I used 5 cans of the green internal frame coating on the rails and cross members, used green so I could see where I did and did not have coverage using an inspection camera. You can use rattle can black spray paint over the green if it shows. As Lotsacubes stated PC looks great. But for durability/repairability go with paint.