I'm sure there are differences that would explain being stuck at login, but I've only tested Beta 3 on two hacks (one with SMBIOS MacMini8,1 and one with SMBIOS MBP6,2), so I don't have much of a sample size. Both of my hacks installed smoothly with one issue: When I logged into my HackBookPro6,2 for the first time after upgrading from Beta 2 -> Beta 3, the login appeared to fail (login returned to the login screen), but after waiting for a minute, the desktop appeared.
After the first login, Beta 3 starts up and logins in without issues.
Note that on my HackBookPro6,2 (which will need OCLP patches for non-metal Nvidia graphics, sound and Wi-Fi), I configured Wallpaper to a static color in Beta 1 before upgrading to Beta 2 and then to Beta 3.
EDIT: The installation of Beta 3 on my HackBookPro6,2 was V-E-R-Y S-L-O-W. I needed to wait longer than expected at several installation milestones. At one point when the Beta 3 upgrade was nearing completion, I waited at a black screen with just a mouse cursor for what seemed like 10 minutes (I didn't time it). Navigation once logged in is painfully slow.
Note that I'm not complaining (and anyone who is complaining about Tahoe on their unsupported Intel Mac needs to learn patience and silence). I'm just reporting my findings for those who are interested.