I can write a book or at least a pretty good paper on the pros and cons of each of laser, label, and inkjet and they all have their issues, but in order of best to worst.

Laser onto a white silkscreen marking square, this is the best for permanency. Legibility (HRI) is very good.  The barcodes, especially 2-D (MRI) can be a little hard to get a good reading on but a good scanner helps.
Best is to have a copper pad, with solder mask and silkscreen over it.
Issues: can (will) expose copper so, cannot cross traces.

For a label, Brady Hi-Temp with thermal transfer and acrylic adhesive backing.  Up to 4 SMT reflows have no impact and actually help label adhesion.  They do NOT like wave solder.  The trick to maintaining the printing is to actually send the labels through at least one thermal profile (apply labels BEFORE SMT). 
* I did a mini-validation for a customer with 4 thermal excursions and 10 wash cycles and maintained legibility throughout.  I also did not lose any labels in the cleaner.
PCB, .062, 4-layer, 1 oz inners, 1/2 oz outers with .001 inch plating, green semi-gloss solder mask.
Label: Brady B-719 Material

Direct Inkjet.  Good process, but sensitive to (1) gloss and over-cured solder mask, (2) PCB cleanliness, (3) proper bake on. (1) Gloss and Over-Cured solder mask do not provide enough anchor points for the printing and can (will) come off in a cleaner.  (2) PCB cleanliness is critical as any dirt, debris or oil will prevent the ink from adhering.  (3) Bake on time and temperature is critical to getting a good set on the ink.  The 2-part inks are less sensitive to (1), but (2) and (3) still apply and a new (4) is in play as depending on application method, these inks tend to smear at the edges.