It almost the difference in TMA and MMA training (broad statement). In aikido, we are learning how to blend and are told that over time we will realise the martial effectiveness (whatever this means). Compare this with an MMA approach - getting in there and having a go at the techniques and over time learning fluidity etc - both get us to the same point, but the MMA approach seems to take less time, which is probably why this approach is more popular these days.
Here's where I would disagree. I do not think both ways get you to the same point. No amount of MMA training will result in the ability to apply technique with "aiki". Yes, really good MMA practitioners get flexible, more relaxed, develop more power but it is an art which is dependent on muscular strength and external power. Getting into competition right away will not result in the kind of re-programming of mind / body required to do technique with aiki.
That said, most Aikido one encounters doesn't really have any "aiki" either. But that isn't because of the emphasis on ukemi as opposed to nage waza. It's because we ask our students to execute very complex techniques, attempting to duplicate something they just saw from the teacher, with no understanding of how to properly use one's body. There is no alternative to either muscling the technique concerned or having the uke tank for you so the technique will "work".
If I were to be left completely to my own devices, I would have the student do static technique, and basic connection exercises of the type one would do with Hiroshi Ikeda Sensei (or any of the internal power teachers) and spend 3 - 5 years getting the body / mind properly programmed. Than I'd start doing more technique in a dynamic fashion. I would not have the student do anything resembling what folks often refer to as "resistant" training until they had been training this way for 5 years or so. I would also teach the ukes to attack using the same principles used by the nage. Right now we have one person attempting to do very sophisticated technique against an attacker who is totally remedial.
I think at the end of 8 to 10 yrs of training properly, we could end up with someone who currently operates at a fairly high Dan rank. In other words, after 8 - 10 years of training we would have someone who functions at or better than what passes for 6th dan at this point.
I wouldn't do any "mixing it up", or sparring before five years or so. Before that the student will fall back into old body habits in order to "win".