I'm not disputing the 300 BO's capability, it has it's place. However, it's a fact that it was designed specifically to be a 30cal, heavy bullet, sub-sonic rd for an AR platform. Nothing wrong with that as it does what it was designed for well. The OP was asking about our thoughts on a caliber in a Mini, not a AR and as Ruger already makes the Mini-30 as well as the 300 BO, he's entitled to hear thoughts on both calibers, despite your 'fanboy' defense of your 300 BO.
What I'm said was true, is factual, and is worth being told despite your objections. If the OP isn't interested in sub-sonic, suppressed performance in his Mini, then the 7.62x39 is likely a better choice for him as cheaper blasting ammo is available and quality supersonic ammo, both fmj and SP for hunting is also available. If the OP is a handloader, then he may appreciate the ability to tune up a bunch of different 300 BO or 7.62x39 loads, however, if he isn't then the 300 BO guarantees that he's forced to shoot expensive ammo as that's all that is available. The 7.62x39, on the other hand, would allow him to shoot a variety of budget ammo, Red Army, Golden Bear, etc. for blasting or plinking as well as excellent commercial fmj and SP ammo from PPU, etc., which costs the same as the 300 BO.
You are correct, I don't have a 300 BO, nor do I have a 7.62x39 either. I just commented on the ballistic performance of 125grn loads for each caliber and the fact that the 300 BO's good performance as a sub-sonic, suppressed rd may be of marginal or no value to the OP. Many of us have no interest in sub-sonic, suppressed shooting. Further, I don't have any bias towards or against either rd, just the knowledge of the fact that the 7.62x39 shooting a supersonic 125grn class bullet produces 200+fps higher velocities. Nothing magic about reading reloading manuals, shooting friend's rifles in both calibers, and generally understanding ballistics.
Edit to add new Hodgdon's Reloading data: It seems that the velocity performance of some new powder choices has narrowed the velocity gap between the two calibers so I thought I'd include the data for completeness. Hodgdon's on-line reloading manual shows that their Lil'Gun (small shotgun and magnum pistol powder) produces 2,402fps with a 125grn bullet in the 300 BO while their CFE BLK produces 2,554fps with a 125grn bullet in the 7.62x39, a 152fps difference.
Why don't I own either? I produce a number of different 30 cal cartridges as I currently handload 30 Carbine, 30-30, 300 Savage, .308/7.62x51, and 30-06 among the 16 rifle and pistol calibers I handload. So it's plain to see that neither the 300 BO or 7.62x39 would fill a need I don't already have filled. Hence the reason I don't own one. That said, I have considered adding a Mini-30 to my collection configured like my Mini-14 Ranch Rifle below as a 'just because' rifle but have a hard time justifying the expense of adding another new caliber.