This is the best answer. One of the keys to this game is patience. Everyone can point to a time when being impatient cost them something. If you need a Tyranitar right now, evolve the 13/15/13 one. I would resist the urge to use the rare candies and just keep walking to power it up. It could be that you evolve it today, and find a raid tomorrow. However, like you said it may have bad IVs. Or you could not find another Tyranitar raid for a month.
If you have no pressing need for a Tyranitar, then wait. Or, make up a deadline. something like, "If I have no better options before _______ I'll evolve my larvitar". That will give you time to decide what you really want to do with your hard earned larvitar candies
To clarify, I've been in this position before. I had been walking a larvitar to get my first Tyranitar and I got candy number 124 the day that raids began. I waited 2 more weeks and got a 91% Tyranitar from my first Tyranitar raid and immediately powered it up. Then I was unable to solo Gengar and Alakazam (still can't quite get Alakazam) so I evolved my original Larvitar despite the raids that continued. I don't regret any of those decisions. It's all about what you need right now.
My current focus is Entei raids (for the Rare Candy and TMs), where a Tyranitar is not that crucial.
Another key consideration is my readiness for Tyranitar raids. I recently returned from a long hiatus, so have to convert my prestiging-optimised lineup to a raid-attacker squad. So far, I have (all L30 wonders):
1. DT/OR Dragonite
2. RT/SE Golem
3. MS/SE Rhydon
4. Count/DP Machamp
5. RS/DP Poliwrath
6. WG/AT Vaporeon
7. Bite/HP Gyarados
8. Conf/Solar Exeggutor
Only Machamp, Poliwrath and Vaporeon are good against Tyranitar. Rhydon would be good if he had EQ, but SE is better for Entei raids. Planning to TM my Vaporeon to WG/HP (which would also make a difference in Entei raids) as it has 15A/14D/14S while my L24 WG/HP Vaporeon has only 10A/15D/13S.
Unfortunately, my Hitmonlee, Hitmonchan and Primeape are nowhere near battle-ready. I will never get a Heracross or Mewtwo.
If you CAN'T get into a Tyranitar raid (which is tough; I live in a major city and even we have trouble getting Tyranitar raids organized) then maybe look at the first one for Evolving. I wouldn't waste anything on the second one at this point - maybe you'll be able to level that one in the future, but for now, that 11A is really low and with the double weakness to Fighting, Ttar's are terrible defenders so only the Attack skill is really useful for Ttars.
Overall I'd still suggest waiting a bit unless you absolutely need a Ttar now. You might be able to get into a Ttar raid and get a comparable Ttar, or you might hatch a better Ttar. Still, the first one isn't a terrible one to evolve.
If you are referring with "my prize is not likely to make much headway in battle" to the appraisel system of team Valor, the lowest possible iv's of a raidboss are alway 10-10-10 and thus a raidboss pokemon is always "strong" (in the appraisel system of team valor, no idea what other colours say)
Similarly, I'm also thinking of powering up another Tyranitar.
I already have a 3400 15/15/11 one with B/C. At my immediate disposal, I have a 15/11/15 and a few other lower not worth it. I also have a 14/14/15 Larvitar... My candies are at 146, I don't mind walking/rarecandyinging if need be.
I don't do ttar raids often. I'm interested in having one with SE.
What would you do? What would Jesus do?