Better? It's not as cut-and-dry as that. They flow the same as 243s (which is great), but have larger combustion chambers. It depends on what you want. If you want higher compression, you can swap on the 243s (or 799s- same exact head, often cheaper because it's not stamped with "243"). All will be the same, you'll just have higher compression. You can't really mill the 317s down to get the same combustion chamber volume as the 243s because the valves will be too close. If you want to run a huge cam or boost, you may want to stick with the 317s. Personally, I like the snappy response of a higher-compression engine and it's better when getting a heavy pig of an SUV moving. If your 6.0 is an LQ4 (lower compression) and you're not boosting, go with 243s/799s. The LQ9 (high compression 6.0) I built for my S10 had 243s on it AND a mild-moderate cam. This put the compression about as high as one would want on a street engine. The LQ9 in stock form requires 93 octane, so my build would've needed that as well as spot-on tuning. These LS engines need stronger pushrods in stock form. You didn't say what type of work the local garage proposed other than pushrods and valve springs. I'm sure that "something else" is a cam. That total package, complete with a dyno tune isn't a bad deal if it's parts, labor, etc. About the only thing that 243s or 799s themselves need at this level is maybe some mild smoothing. I'd strongly recommend a trunnion upgrade kit on the stock rockers if getting a performance cam and the accompanying stiffer valve springs.
Cliff notes:
243/799 or 317 heads- doesn't matter any further than what you want for compression
Performance cam- need stronger pushrods, appropriate valve springs, trunnion upgrade, custom tune