Heck I’d trade invisibility just to undo the vincing I’ve already gotten, let alone the guarantee of no more.
(I suspect that there’s a correlation between choosing invincibility and age. When I was 20, I probably would have thought harder about it).
I’d take invincibility. Temporary pain doesn’t scare me just the long term injuries and death. If that were removed I would make a killing as a stunt man and daredevil extraordinaire.
Invisibility would be fun for a bit but once you’re old you’d just end up using it like Bilbo to avoid unpleasant encounters. But if you could still be out hiking, waterskiing and diving into volcanoes when you’re 70 the fun would never end.
ETA: I’m 26 by the way.
Invincible. If I were invisible, someone might do something that would hurt or kill me because they didn’t know I was there.
Invisibility. Invincibility without super-strength, immortality or lack of pain is not for me, and any fighting I do do (SCA), it wouldn’t matter since it’s all on the honour system, anyway, so it’s no advantage. Whereas invisibility would suit my other hobby interests just fine - I like birdwatching. And if it could include objects, even better - I also like taking photos.
This. I ride a motorcycle to work so this is a clear cut call.
I’m already invisible. Invincible might be nice for a change.
You don’t get an invisible motorcycle to drive around. 
Could I have a little of each? Like, really tough and kind of blurry?
I’ve often wondered, to be invisible light must be able to pass right through you, right? This includes your retinas. If light is passing through your retinas and not impacting on them, you’d be pretty much blind.
Invincible.
Invisible? You gotta be visible sometime, buddy.
I’ll go for invincible, and basically just try to stay out of too much trouble. I could disappear into the wilderness and not starve, freeze, get eaten, etc.
For those times I was at risk of maybe being captured, I could strap some nasty explosives on that would make my getaway easier.
Oooh, that may have decided it for me. Fun times.
Invincible. First thing I’d do - running with scissors!
Nope, invincible for me. You don’t have to be a superhero or a super villian to make it pay, just effect some sensational rescues and the fame and money will follow. On the otherhand, some wiseguy with a laser thermometer will be able to pick you right out, because I assume in order to be completely invisible, that you’d also have to be au naturel. Further, if you lived somewhere that there was winter, you’d have to breathe outside at some point, so…
I’d take invisible-as-qualified-here over invincible-as-qualified-here. You can use the former without anyone being the wiser, but as soon as you attempt in any way to capitalize on the latter, people are going to know about it, and something tells me it wouldn’t end well.
If invincible fixes the damage already done to my back, then I’d pick that. But if it’s just nothing further can be done to me, that’s harder.
On the one hand there’s being certain that nothing could make me leave the Celtling before she’s ready to fend for herself, a strong draw.
On the other hand, living so close to DC I could accomplish really major good in the world by listening and reporting invisibly. This has to assume though that I’m also invisible to heat sensors and other such detection equipment.
So yeah, back fixed = invincible
if no, then
All sensors included = invisible
if no, then
final decision = invincible
Even I don’t think I could be trusted with either.
I feel invincible, but I also feel invisible at times. I’d like to beat the crap out of people who make me feel invisible. Ergo, I’d opt for invincibility.
After beheading:
1: “HE HAS NO BLOOD!”
Invincible: “Yeah, well get me some tape”
1: “What?”
How could you survive being beheaded? Nevermind, there are too many movies that answer that for me.
Presumably if I’m invincible, I can’t drown? I’ll take invincibility and use it for quite mundane profitable things like pearl diving.
Invisible is probably more immediate and intense fun, but with an increased risk of injury (cars won’t slow down for you), so invincible it is.