It looks like you might be confusing some terms here... using more battery/power doesn't necessarily translate into more or less radiation. The radiation strength is determined by the frequency that the devices operate at, i.e., the frequency of the radiation they emit.
3G devices (in the U.S.A.) don't really have a set frequency, but rather will operate at various levels ranging from ~800 MHz to just shy of 2.4 GHz (more if you're using Bluetooth or 4G phones). WiFi signals, on the other hand, share the same general frequency as microwave ovens at right around 2.4 GHz.
But because of how we use these signals, it becomes a battle of distance and duration. Cell phones are right next to our skin for short bursts of time, while routers or laptops generally sit far away from us for extremely prolonged periods of time. The UK's Health Protection Agency noted in 2007 that:
sitting in a wi-fi hotspot for a year results in receiving the same dose of radio waves as making a 20-minute mobile phone call.
But the thing to pull away from all of this is that you probably don't have to worry too much about this kind of radiation having any seriously dangerous long-term (cancerous) effects on you (provided you're not walking around with wireless devices taped to every inch of your skin). That's not to say long term exposure to low-level radiation might not have other adverse health effects, but it's hugely unlikely to be cancer. Any radiation below ultraviolet (radio, microwave, infrared, and visible light) is non-ionizing and won't penetrate bone, meaning it can't break down atoms (and consequently DNA, leading to cancer) and it can't get to your sweet, delicious brain. The "do power lines/microwaves/cell phones/next radiation-emitting-device-that-most-people-don't-fully-understand give you cancer?" studies are all, as they'll always be, resoundingly inconclusive.
Even the newest WHO review of cell phones (described by CNN with a typically alarmist title) somehow makes the claim that cell phones are "possibly carcinogenic to humans," despite the fact that "The WHO work group did not find that there was sufficient evidence linking cancer and environmental or occupational exposures with microwave energy," implying that the possible carcinogens must come from the phones themselves, and not the radiation.
Also worth noting is that the WHO group also puts coffee, pickled vegetables, and tea into the same classification. There's a lot to be worried about in the world; this probably oughtn't be too high on anyone's list.