The difference with method 1 is that, with method 1, you're not actually converting anything. You're erasing the existing data and replacing it with an encrypted partition. With method 2, a conversion process begins, which doesn't erase data, but does take more time.
The thing to keep in mind: any drive which is converted from a normal drive (HFS+) to a Core Storage drive can be reverted back to a simple HFS+ volume (non-encrypted). If you use the Disk Utility method you showed above, the resulting disk will NOT be revertible, because the disk will have never been an HFS+ volume in the first place. That is what you're seeing with "Revertible: No". If you use the Finder method (or the equivalent command-line option), the drive will be revertible.
Another thing to keep in mind is that modern versions of OS X will normally use Core Storage on the boot drive by default, even on unencrypted disks. The result is that, in some cases, "Revertible" may always be "No". You'll always be able to decrypt a Core Storage volume however, so perhaps this is insignificant for most people.
If you want to talk about what's the best option for Time Machine, it doesn't really matter. The end result is, in either case, an encrypted disk, protected by a password. To do anything to the disk you would need the password. There isn't any significant difference to either method. It's marginally possible that the disk utility method could be the slightest bit more secure, for the simple reason that this reduces the number of attack vectors. If there is any benefit, it would only be slight.
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Speculation: The view button is missing because disk utility defaults changed and now everything is viewable by default.
As for the greyed out partition button, notice that the external drive tab has two levels, a parent and a child. The 'partition' button becomes un-greyed-out again if you click on the parent instead of the child. This seems to be working fine now.