Louis,

I prefer dipping in fillets because I can see the root fusing fully.  There are also *some* instances where the cosmetic ripples are required.  But laywire technique can produce welds of the very highest quality as well.

Laywire makes for nice looking fillets on lap joints in sheet metal in my opinion.

The only exception I can think of is AC  GTAW with aluminum... The dip technique is required here because a lay wire technique would prevent the cleaning action required to remove the oxide coating on the aluminum.

I agree with Lawrence that either are good techniques, but I would add assuming a well trained welder.

I have seen a fair number of welds on steel that lacked fusion at the root or between beads using the laywire technique because the welder:  Used a filler rod that was too big in diamter, wasn't washing that puddle out wide/thin enough, and/or had the current too low.

Inexperienced guys sometimes have particular trouble with fusion with this technique down towards the bottom of a groove weld, especially in the flat position such as on the top of a 5G pipe.

For an inexperienced guy on heavier sections I think dipping tends to be a little more forgiving.

Hey Louis,
As Lawrence has indicated, "BOTH" techniques can provide sound weldments, although practice on thin material, especially aluminum, will render optimum results. For the custom polished aluminum diamondplate(.062) crafts I make, the corners are TIG welded using the "laywire" technique simply because of the thinness of the corner joint & the aesthetics needed. The corners are polished to match the material surface. Here are a couple pics to show you the joints & the finished results. I have never had a joint crack or break using laywire fillets. You will find that the filler diameter is the secret for a good laywire weld & on the thin corners, I use a piece of steel angle as a heat sink that helps eliminate any burnthru. Here's some pics....

Denny

As mentioned both are valid for specific applications.  I would say outside of open root groovve welds you won't see people laying the wire in the groove. This is mostly due to the inability to control fill amount. 

the lay technique is often used in sheet metal welding to prevent burn-thru on thin sections. In cases such as an outside corner gap, the lay technique gives a thicker material to burn through, instead of the thin joint that tends to pull-away. Outside of using it for thickness control I generally preferred dipping.  We would sometimes use thicker 3/32 wire to do fill passes on pipe welds or other groove welds, but i would caution it due to the higher liklihood to create defects.