Rooting, in and of itself, won't affect battery life at all. Rooting changes nothing on your phone, it only gives you access to files and folders that are normally locked. It's possible that something you froze is a process that another app or process is trying to execute.
Realistically though, based on the battery stats you provided, I don't see anything that stands out. 40 minutes isn't a long enough period of time to really tell anything, and the screen is your biggest battery user. That means nothing else is using very much battery. Also, 100% doesn't always mean 100%. See this:
Your battery gauge is lying to you (and it's not such a bad thing) - xda-developers .
This is why many new phones will "lose" up to 10% within a few minutes of coming off the charger. The reality is that the battery was only at 100% capacity for a brief moment, after which the battery management system allowed it to slowly dip down to around 90%. Leaving the phone plugged in overnight does not make a difference: the phone only uses the wall current to maintain a partial charge state.
So even though your battery gauge said 100%, it might have been only at 96% when it came off charge.
Wait until it's down to 50% or less of full charge, and see what the stats look like.
edit: Oh, you asked about ROMs. IMHO, (or not so humble

) the best ROMs for the Galaxy S3 are those based on Touchwiz, and the best of those are Wicked Sensations and M.O.A.R. I'm currently running M.O.A.R. Most of the bloatware is gone; some of it can be added back if you want. Both WS and MOAR offer tremendous customization options, too.
MOAR:
http://forums.androidcentral.com/sp...ting-roms-hacks/253237-anybody-try-m-o-r.html
Wicked:
http://forums.androidcentral.com/sp...wicked-sensation-jellybean-v-3-0-mb1-rom.html
If you're looking for a more vanilla Android experience, I haven't tried any of them, but these threads might help:
http://forums.androidcentral.com/sp...ere-no-aokp-rom-sprint-samsung-galaxy-s3.html
http://forums.androidcentral.com/sp...ks/254128-there-any-aosp-roms-sprint-gs3.html
The most important rule of all when flashing ROMs is this:
ALWAYS, without fail, be 100% positive the ROM you're flashing is intended for the Sprint SPH-L710 Galaxy SIII. Many ROM developers aren't very good at identifying what devices their ROM is for. Flashing a ROM for a GSM phone (international i9300, AT&T, T-Mobile
will hard brick your phone.
Regardless of what ROM you decide to try, my advice is to read the threads here on A|C and, especially for MOAR (which doesn't get a lot of coverage here), on xda. Make sure you understand what you're doing. If you're not sure, ask questions. (Ask here first. XDA isn't the most friendly place to noobs.)
ALWAYS make a nandroid backup of your current, working configuration before flashing a new ROM or customizing one.That way if something goes wrong you have an easy way to get back to where you were.
Spend a bunch of time reading the threads in the rooting forum here (you are on Sprint, right?):
Sprint Galaxy S3 Rooting, ROMs, and Hacks - Android Forums at AndroidCentral.com
Understand that these ROM developers, while very, very talented, don't have the resources to do the kind of testing that Samsung and Sprint do. We are their testers. WS and MOAR have been around long enough they're very stable, but a new version likely will introduce some bugs.