Don't think that I am talking about apps from other companies, if so this post will be deleted by someone soon.
1) The original Logos app
2) http://library.logos.com/ (or http://library.logos.com/?beta=false after you use 3) 
3) http://library.logos.com/?beta=true (you cannot save it in the bookmark, it will only save library.logos.com, so you need to memorize ?beta=true. If you don't need to switch back to ?beta=false again, then do it once will work forever) 
4) a remote desktop app, to get access to Logos4 in a Windows based computer (Mac also works, but currently Logos in Windows is the most powerful)
Let me explain it:
1) the Logos app is a bit more than a ebook reader, the good thing is that you can download the ebook offline.
2-4 requires internet access
2) occasionally, it can be better than the app, e.g. reading Chinese Bible, where the app has error on indentation.
3) much better than 1-2, looks very similar to your Logos4. But no reading plans, etc.
4) Full access to your own Logos4, using one of the following apps:
  Normal
  0
  false
  false
  false
  EN-US
  ZH-TW
  AR-SA
  MicrosoftInternetExplorer4
| 
 iteleport 
 | 
 24.99 
 | 
   
 | 
| 
 Desktop connect 
 | 
 11.99 
 | 
   
 | 
| 
 Mocha VNC Lite 
 | 
 free 
 | 
   
 | 
| 
 Mocha VNC 
 | 
 5.99 
 | 
   
 | 
| 
 Remote Desktop Lite 
 | 
 Free 
 | 
 Remote Desktop 
 | 
| 
 Remote Desktop 
 | 
 5.99 
 | 
 Remote Desktop; related to Mocha VNC 
 | 
| 
 LogMeIn Ignition 
 | 
 29.99 
 | 
   
 | 
| 
 Connect to PC  
 | 
 4.99 
 | 
   
 | 
| 
 VNC viewer 
 | 
 9.99 
 | 
   
 | 
| 
 iTap VNC client 
 | 
 7.99 
 | 
   
 | 
| 
 iTap RDP client 
 | 
 11.99 
 | 
 Remote Desktop 
 | 
| 
 Wyse PocketCloud Remote Desktop & RDP Client 
 | 
 14.99 
 | 
   
 | 
| 
 Jump Desktop 
 | 
 9.99 
 | 
   
 | 
| 
 WinAdmin 
 | 
 8.99 
 | 
   
 | 
| 
 Remoter: Remote Desktop 
 | 
 0.99 
 | 
 Remote Desktop 
 | 
| 
 Wormhole Remote 
 | 
 6.99 
 | 
 Mac only 
 | 
| 
 PC Access 
 | 
 2.99 
 | 
   
 | 
 
 
 I haven't compare which one is better (since I am not rich), nor I find any review of VNC app on iPad. I think iTeleport and Desktop Connect are the most famous one. I will use Mocha VNC Lite now since it is free and wait for some review to compare them.
To setup the Mac/Windows, go to here (which is the setup documentation from iTeleport): Windows/Mac.
To conclude, using all 4 methods helps in different ways to your Bible Studies. 1 can be offline; 4 is most powerful, allowing you to access all your resources, but you need to turn on your desktop at home first; 3 seems very good in between, 2 might be useful sometimes (but 2 and 3 cannot be used at the same time). But since the iPad does not support multitasking yet (will be in Fall), you can't use 1, 3, 4 all at the same time.