I replaced a 48" x 16" double-tier pedalboard with an Axe-FX. The board was heavy on delay and reverb (something like half of the total FX, IIRC) and had the full Boomerang III setup (all three pedals).
The AFX rig that replaced the pedalboard is just an AFX II XL+ in a 2U rack case plus a LF+ Pro+ controller.
I made the change mid-March, so I can tell you with some clarity what are the tradeoffs.
1) Cost: AFX/LF+ is less expensive.
2) Weight: That pedalboard is a bitch to carry. The AFX rig is not.
3) Random Contol: Every pedal has its own knobs. If I want to change something on-the-fly, it's an immediate action. Reach for knob and turn it... With the AFX/LF+ rig I can program anything I can anticipate, but extemporaneous changes are pretty much off-limits.
4) Programmed Control: Advantage to the AFX/LF+ rig, for obvious reasons. Yeah, I suppose I could've added a programmable loop pedal to the pedal board, but that would have made cost, weight and random reprogramming even less advantageous.
5) Sound: both rigs sound great.
6) "Special" pedals: This is where there's no contest. There are certain pedals that I simply can't duplicate with the AFX. (The guy at EHX who designed and programmed the SuperEgo and the B9 deserves an award.) I have what I consider to be a pretty good-sounding Hammond patch for the AFX II, but I can't get it to track anywhere near as well as the B9. And while I've learned to adapt a hold-delay on the AFX to replace some of what I did with the Superego, it's just not the same... Likewise, the AFX looper is no competition for the Boomerang III. (I've learned to deal with the limitations.)
7) Stacked effects: While I *usually* exercise restraint in enabling a bunch of effects all at once, there are times when it *might* make sense to -- for example -- kick in all the ambience pedals at once.
There are limitations (this was mentioned earlier in the thread) to how far you can take that with the AFX. I've learned to adapt.
In the end, I see the AFX rig as a net win over the monster pedalboard. Yes, there are some things the AFX can't do. (OK, to be fair: lets say that there are some things for which I haven't been able to create an AFX patch to my satisfaction.) But it does more than enough to be useful to me.