I got a problem.
I'm going to the auction House and engaging in bidding wars while doing money levels to get some more riches.
But it always gets bought while I'm offline.
So should I just go to Basil for the recipes myself or continue my current plan?
Well actually I'm currently doing Starnum 3 and 4.
Anyway i figured out in the time that it takes me to get to Basil on Easy is more then the time it takes for me to finish RJP on Elite.
So yeah.
Two important factors for these dilemmas are:
1. Having fun.
2. Personal efficiency.
Is it worth repeating a mission to get crowns faster [to buy that recipe]?
Having fun far outweighs getting items faster for me. It may not for you.
The two links that Bopp supplied identify the more optimal areas for harvesting crowns.
If you do go the arcade route, be sure to play the depths after Basil's shop... as they pay roughly double the depths before the shop.
To my knowledge, there is no public analysis of the frequency and quantity of the contents of Basil's wares to give an answer more exact than that.
You could do both, simultaneously.
Run the gate that leads to the boss you want to face, starting at Moorcroft and ending at Emberlight. You'll hit Basil for some recipes, and then proceed onward for the boss fight. I've been doing this for a while now, searching for a certain 3* piece of gunner armor.
Just running the arcade stratum to basil works fine, but you can go to emberlight for the extra crowns
Personally, I've been forced to arcade run because no one has put a sacred grizzly guerilla armor recipe at the AH, and ive gotten a good amount of crowns joining randoms and continuing to basil
Much of the raw information you want is Lancer Knightz' mission data and Skepticraven's Arcade data. But the latter does not include recipes found.
In general, even if you don't personally want any recipes, Arcade runs can be quite profitable due to recipe reselling. But this involves effort (learning Auction House prices) and risk (sometimes not being able to sell recipes for no apparent reason).
So I don't know the answer, but my advice is to run the Arcade most of the time, because missions get boring quickly. Save missions for those times when Arcade Stratum 5 is filled with lame levels.
Also keep in mind that (ignoring recipes) Stratum 6 is generally more profitable than Stratum 5, especially if you need Radiants. Try to do arenas and danger rooms on Stratum 6.