And another update on this:
Current nightly builds (since 2018-03-15) should at least in theory now support the RPi 3+, if everything works as it should however has yet to be determined.
I'm running Webmin on my RP3, running Octoprint. I watch the CPU utilization when doing various things in the system. For example, when I upload gcode, I watch the CPU spike to around 75% while it's assessing metrics for print-time and cost analysis.
When it's printing, I don't see the CPU spiking more than 12%-15%. So, that leads me to believe that the current model should be MORE than sufficient to carry out your regular printing tasks; along with some other things, if you so chose.
This is also while I have Printoid (Android) running on my phone, connected to Octoprint. AND running the webcam stream in my desktop browser.
It should be good...
I don't see this as any benefit to octopi, but it should make my Kodi box happier!
My mistake , it is just the ordinary 3B that they sent , FALSE ALARM 
this morning i have running the octoprint nightly 0.15,and it works now
0.14 will not working for me.
but if i press print knob in octoprint,then the print is blue en still blue,en not the cancel or pause.
sorry my english is not good 
I was semi-stupid and got the 3 b+ and now the link for nightly builds does not work atm.. http://gnethomelinux.com/OctoPi/nightly/
gives me: ERR_CONNECTION_TIMED_OUT
Probably due to this
Until the page comes back up, this image at least was reported to work on this OctoPi ticket.
Hello guys, I got an RPI B+ and installed the Nightly Builds "2018-03-23_2018-03-13-octopi-stretch-lite-0.15.0.zip" on that...
But, on the download page I see the new version: 2018-03-26_2018-03-13-octopi-stretch-lite-0.15.0.zip, so the question is, how I get the update from my version 2018-03-23 with the new relese 2018-03-26..???
I need reinstall all things or the sistem is able to update it...?
Thx for your help...
Hi, I have just found Octopi and have tried loading it on to a Pi 3+, however no joy.
After creating an SD card with 0.14 and powering it up it appears to have a problem as the red LED flashes a pattern. I haven't had time to attach a screen yet, but intend to do so tomorrow. If wanted I will supply the screen messages.
David
@Macca45 I suggest you read the article again which clearly states that OctoPi 0.14 won't work with the Pi 3+ 
Yes I had just found that where you said you did not expect it to work. I was merely confirming that it doesn't work.
Ah, ok then. It sounded more like "why isn't it working" - and you wouldn't believe how many people already actually didn't read the article and then opened up support requests, hence my assumption this was the case here as well.
For image updates you usually need to reinstall. If it's just a new base image, the usual ways of updating a Raspbian image incl the kernel might be enough though.
So I just got a 3+ and trying to print with octopi/octoprint. I don't think the latest stable one works... I got the image in via both etcher and windisk imager and when I put the card in, I get a flashing red light and rainbow screen... Going to try a nightly now 
2018-03-30_2018-03-13-octopi-stretch-lite-0.15.0.zip
seem OK
=> boot OK , wifi OK
As a point of information, bought a new Pi3+ to run OctoPrint, but the Pi would not boot. Seems a setup that supplies ample power to the older Pi3 does not work. So there is something different in the power requirements of the new Pi3+. Have not yet puzzled out the difference.
Swapped in an older Pi3, and now have OctoPi running (my first use of OctoPrint).
Pi3+ needs a completely different build, libraries and drivers. Using anything below the nightly Octopi 0.15 builds will not work. It’s not power, just a different chipset.
It requires a later version of Rasbian and NOOBS too. You cannot take a build for a previous Pi version and plug the card in. The 3+ just won’t boot with any of them.
It’s a start from bare rebuild. The good news is that Octopi 0.15 builds work just fine. I just added the desktop GUI to make configuring the WiFi/LAN easier at the time.
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For what it's worth, I downloaded the latest nightly OctoPi image onto a microSD card and threw it into a Raspberry Pi 3 B+, edited the /boot/octoprint_wpa_supplicant file (making sure to edit the wi-fi country at the bottom) and it joined my wi-fi without problems.
I also note that I next ran sudo raspi-config from an ssh session and the wi-fi country in the localisation section was still GB so I set it to US (as well as the timezone, locale...)