I see this question all the time. Read on for an outline of the common arguments in favor of each rating and a glimpse of my perspective on this important aspect of Sniper gameplay.
Here's the short answer: you want both.
The long answer is that what you want is situational based on your level, your skill tree, and your currently available gear and balance of stats (shocking, I know). Let's review some of the most common opinions you'll hear from both players and theorycrafters.
Arguments for Crit Rating over Power
1. Sniper DPS is highly dependent on frequent critical hits. An increased critical chance also takes advantage of the skills that increase the base critical damage of Marksmanship abilities like Followthrough and general Sniper abilities like Series of Shots, and Takedown.
2. Some of the most damaging Sniper abilities are single-target. A high critical rating benefits these abilities.
3. A high surge rating dovetails well with a high critical rating. Sniper gear tends to contain a fair amount of surge.
Arguments for Power over Crit Rating
1. Power increases the damage done by normal (non-critical) attacks. For much of the leveling process, you will be getting fewer critical hits than normal ones. Power rating will therefore increase the amount of damage you do as you level.
2. Some armchair theorycrafters (aka: more math than Sniper experience) will tell you that it is better not to depend on critical hits for damage despite the indisputable fact that Sniper is a strongly crit-dependent class in a variety of ways. I've heard many people argue that Sniper's cit-dependence works to its disadvantage. This may or may not be true. All I know is that Sniper is a very strong candidate for endgame raid DPS.
3. Lethality Snipers benefit from Power because of how often their DoTs tick. It's reasonable to assume that many will be "normal" DoT ticks rather than crit. Increasing the damage of the normal ticks by a small amount will result in a significant overall increase in DPS.
What really happens with your gear is that it purposely (by design!) evolves over time. The lowest-level gear contains only Cunning and Endurance and Tech Power. These are Sniper's base stats. Accuracy rating and power are introduced early in the leveling curve for precisely the reason I've mentioned above: at low levels you are more likely to hit for normal damage than you are to crit. You are also more likely to miss. Gear with accuracy and power helps you the most at lower levels.
The midgame and endgame are where critical rating and surge rating start to put in an appearance. At this point you should have a sufficient amount of power to start building more and more critical rating as you approach the endgame and begin to get more skills/talents (i.e. Between the Eyes in the Marksmanship tree) that increase crit damage or crit chance. This shift in your gear will complement your talent choices in your tree. Incidentally, this gear evolution is another reason to go straight up to the higher tiers of your spec. Your gear is designed to complement your leveling progression and is guaranteed to function well with most "pure" builds.
NB: Bear in mind that getting behind in gear upgrades will have a negative impact on your damage output. The shortcut to improving your gear is looking for something with a higher armor rating. The planetary commendation vendors on the Fleet Station (both mod and equipment) are a good source of options as you level.
Sniper Build Specifics
Marksmanship Snipers are heavily crit-dependent in general. Many of their skill bonuses either increase the likelihood of critical hits for certain abilities or outright increase critical damage.
Engineering Snipers have hard-hitting single-target abilities with some AoE and DoT. They benefit from a balance of crit rating and power, but many players seem to prefer one or the other (and it is possible to build for either preference).
Lethality Snipers are an interesting breed. Typically a DoT class would want more power. However, the Lethality tree's energy regeneration skill, Lethal Purpose, is based on the critical hits of DoTs. A high tech crit rating is important in order to get the most benefit out of Lethal Purpose.
Every spec is more or less dependent on both crit and power. It would be very hard for me to make a blanket statement prescribing one over the other.
In the endgame you should have amassed something like 25-28% ranged (white) crit rating and about 27-30% tech crit rating as a baseline. It is at this point that you can start rebalancing power on your gear and making real decisions about what to use.
I'll preface this by saying that I am currently progressing through Operations content (Normal, Hard, and Nightmare) with my guild. My recommendations are based on personal observations and experience. My raid gear still needs some work, but it's starting to come together in interesting ways. The following are the most significant new elements for DPS to consider:
NB: I currently have a flat 40% ranged/tech crit chance from gear.
1. Relics. These offer large temporary bonuses to many ratings. Which you use is situational.
2. Biochem-only crafted reusables. This craft has been pretty nice for me as an endgame DPS. I have a Rakata reusable cunning/power stim and a reusable medpack, both with bonuses you can't buy on vendors. I'm working on crafting a reusable adrenal.
3. Movement and enrage timers. You need to be able to squeeze as much DPS out of your build as possible while also using defensive cooldowns responsibly in order to beat enrage timers. It's easy to drain your energy if you're not careful, so being good at this part takes a bit of experience.
4. Operations gear. It's pretty balanced between crit/surge and acc/power (you'll find them as pairs most of the time). It has a mix and doesn't privilege one too far over the other. I decided to take the hint. If you're curious, the "Sniper-specific" endgame gear is the "Field Tech" set in Tionese, Columi, and Rakata flavors.
I'm an objective-focused PvP player so my tactics may be a little different than most. I defend turrets in Alderaan, I stop and/or kill ball carriers in Huttball, and I camp doors in the Voidstar even when my team has moved into the open area to dominate their opponents.
Depending on what cooldowns are available (stims, relics, defensive abilities), having a balance of crit and power allows me to play more aggressively and increases my DPS in general. I can comfortably use all of my abilities without fretting that one doesn't crit enough and another doesn't have enough power to provide worthwhile damage.
There is no easy way to privilege one rating over another. Which rating you need varies according to your level, spec, and your current needs as a DPS player. The issue becomes moot in the endgame because the gear sets are pre-balanced to favor neither stat. I've said it before in other posts, but it bears repeating here: the effects of stacking ratings or stats have been consisently nerfed throughout beta and will likely continue to be nerfed after launch.
Your safest bet is to balance your stats.
(I continue to believe that alacrity on gear is more for healers than Snipers, but that's an issue for another post!)
Comments, questions, or corrections? Leave them in the comments section here or email me: Fentanyl213@gmail.com.