Both are recognized knots.
The top knot is called a "bowline with a bight" in the knot bible "The Ashley Book of Knots" (aka "ABOK"), where it is depicted as knot #1074 - ABOK #1074 in knot-nerd parlance (although Ashley's usage of this knot envisioned the bight "tail" actually being loaded, this name is generally still applied among those who use this as a mid-line knot, especially in the rope-rescue world, which is my primary affiliation).
The bottom knot is called a "bowline on a bight" in Ashley (ABOK #1080).
One key difference is that the "bowline with a bight" can be tied around a fixed object, whereas the "bowline on a bight" cannot. Another difference (as preventec47 observed) is that with the bowline with a bight, if the bight "tail" is continued with a "Yosemite finish", you create a forward-facing loop that can be loaded, which significantly increases this knot's versatility.
Both knots can be expected to have similar strengths when used as "end" knots (two-way load, loop loaded against standing part), because testing and field experience show that overloaded knots generally fail at the first tight-radius bend in the knot coming from the standing part (loaded strand), not in the loop itself.
I actually just used the bowline with a bight today to connect a winch cable as the "haul" force for 2:1, 3:1, and 4:1 mechanical advantage systems in 11mm static rope to pull an uprooted stump, and can attest to the ease with which this knot can be untied after experiencing a significant load (in my case today, on the order of 1,000 lbf). The bowline family of knots is nearly unrivaled in their ease of untying after loading, which is also why, when tied in a configuration that has a tail, bowlines should be backed up if used for human life loads or if they may experience cyclic loading and unloading.
