KTP Laser Vs. IPL for Broken Capillaries on Face?

KTP Diode 532nm laser or Pulse Dye Laser (PDL) are the standard of care for broken capillaries or telangiectasia on face. IPL or fotofacial laser can be helpful to fade pigmentation and rosy complexion.

Treating redness on the face often means treating various sizes of capillaries. For general diffuse redness, the IPL is more effective and efficient. For solitary vessels such as those found around the nose or on the outer parts of the cheeks, the KTP laser or pulsed-dye lasers work better. It is best to plan on a series of 4-5 IPLs and 1-2 treatments of the KTP or PDL lasers mixed in.

IPL is superior for the diffuse erythema of, say, rosacea. However, if you are seeking a remedy for the fine telangiectatic vessels which you seem to be describing, I prefer the KTP laser or a pulsed dye laser.
Also, you might consider electrodessication. While not as high tech and glitzy, it would also be effective and far less expensive than the above two solutions.
I am not sure what you mean by the brownish lesions below your eyes. Telangiectasias are generally not described as being brownish. Thus, I cannot provide a recommendation for this problem.