Having loaded a lot of both calibers, hee is what I have gotten over the years.
With the 30-06 you can get by with neck sizing the cases to an extent when using factory chambers. I generally load one lot of cases for that particular rifle. My loads are generally up towards the top end but not over published levels. About every third or fourth load I have to set the shoulder back in order to allow them to function properly. In my sizing I start out with a full lenght the first time. The next load I generally have the die shimmed up between .020" or .030", which allows me to get the majority of the neck as well as some of the side wall of the case, but not all the way down to the head. I do this for the next couple of load till I can feel the change in the bolt upon chambering them. After the case becomes snug to chamber I simply put the die back in with out the shim and set everything back to the proper size.
As for the .303, your correct in that most of the chambers are oversized and when you full length size the cases they generally seperate after about the third load. However I have had some seperate on the first reload load as well. It is advisable to get one of the stuck case extractor if your going to load a lot for them. They aren't much and act like a inside bearing puller of sorts. You simply remove the broken piece of the case head, then drop the extr5actor in behind the case, and close the bolt enough to allow it to grab the front end of the neck. One it does you extract it as if it were a spent case. Some are adjustable and you might have to try it a couple of times to get the right tension, then once you do add a drop of super glue to hold it. They aren't expensive and sure save a lot of head scratching and possible damage by other means.
CJ Weapons Broken Shell Extractor 303 British
On the dies, I set them so that I can get the neck sized about two thirds of the way down to the shoulder. This has allowed me to get up to 5-6 loads from both Rem. and Win. cases. I normally use Winchester for most of my loading but have found that with my particular .303 that the Rem. cases actually hold up better. Probably due to the extra metal in the web area. I do not load to full power loads and generally use IMR-3031 for 150gr loads. I worked it up from data in the older Lyman manual and have left it alone as it shot good through the years. I also had good luck using the Remington bulk 180gr CL's as well. I don't shoot them as often, but the ones I loaded shot well and killed deer very effectively.
Good luck and keep you pressures down on the .303 and you should be good to go. Just keep an eye on the wall area just ahead of the bases and you can generally see right where they will seperate. It might take a few rounds to get the die set but once you do, your in business. IF you can load at the range that helps out greatly.
Here is a link to some info on the .303 that you may or may not have already found. It could definately help out on some of the areas you might have questions about.
.303british.com/
