I like the first one better by far. Nice style and compact nature. You could even eliminate the = in the heart part and just have the numbers next to it.
If you aren't going to label PLAYER and ENEMY on the bar, the boss bar should not be in the HUD. I'd say it would settle better to have the boss bar only appear when fighting a boss, perhaps on the opposite side, and not connected to the player's status HUD.
An addition note:
Since you did color Trevor into a higher color count than everything else, you should probably up the colors of the other things too. Style consistency is important to creating good aesthetics. I like the retro higher color look, but it looks weird seeing it along with strict 2bbp (4 color format) NES pixel art.
The color and shading progression also seems different. As to say, the colors on Trevor are more realistic, and less bright cartoony, while the ground colors are bright and cartoony. The ground's lightest shade, make that less saturated and it would probably match Trevor a lot more.
Either that or revert Trevor back to 2bbp standards. But I really like the high color retro look. I'd be interested to see how the whole thing looks in that style.