How "powerful" is a wing tip vortex?
If we're talking about large aircraft the answer is Powerful enough that you want to stay out of them.

I refer you to this delightful FAA video in which a Cessna (looks like a 172) was flown into the wake of a C-5 Galaxy. The Cessna was rolled through 360 degrees by the vortex.

NASA research has shown that the rotational speed of wake vortices can exceed 150 miles per hour (130 knots).
While the Enhanced Fujita Scale rates tornadoes based on damage a 150 mile per hour wind speed is in the range estimated for an EF3 tornado ("Severe Damage", defined as Entire stories of well-constructed houses destroyed; severe damage to large buildings such as shopping malls; trains overturned; trees debarked; heavy cars lifted off the ground and thrown; structures with weak foundations are badly damaged.) - This should reduce your desire to be anywhere near the wake vortex of a large aircraft.



If we're talking about smaller aircraft (say two Cessnas flying in trail, and the trailing aircraft somehow gets below the lead) it's strong enough to be unpleasant - the wake from the leading aircraft will shake and rock the wings of the trailing aircraft, but it probably won't flip the trailing aircraft over.  

Many pilots are familiar with encountering their own wake at some point in flight training: It can happen when practicing steep turns in calm air.
If the weather and timing of the turn are "just right" and you produced a circle rather than an oval yo will hit the descending wake from your outside wing as you roll level at the 360 degree mark. This produces a slight "bump" at the end of the maneuver (visible in this video).