I would say that D1 ACHA teams would probably beat D3 NCAA teams. While some ACHA teams are nothing more than clubs, others seem to have strong university support. I'd say that that D1 ACHA is probably somewhere between D3 and D2 NCAA hockey.
I've also played ACHA hockey, have NCAA DI and III friends and seen all the different levels of college hockey from ACHA D3- NCAA DI. I've played at the ACHA level, and am a strong fan and supported of ACHA hockey. but I'm also real and honest, as much as i'll support and stand up for any idiot that trashtalks ACHA hockey its generally not at the NCAA level.
ACHA DI (and some of the top and highly organized D2 teams((that'll prob jump to ACHA DI in the next few seasons)) could compete at the NCAA D3 level. The top ACHA teams would be mid-level NCAA D3 teams at best.
The ACHA has come a long way over the past years and continues to grow in organization, teams, and talent. Give it 5-10 years and it might be a more equal playing field btwn ACHA DI and NCAA D3.
The ACHA is a viable, cost effective way for universities to field competitive hockey teams. Especially with the exclusive atmosphere around NCAA hockey.