You'll find that the types of steel covered by D1.5 is limited compared to D1.1, although it represents the common D1.1 materials.
D1.5 doesn't provide for prequalified welding except with Low hydrogen SMAW electrodes.
D1.5 fracture critical PQR's are good for only 36 months, but you weren't going in that direction anyway.
Up to 5/16" fillets must be single pass welds (heat input control).
The no grinding requirement on welder qualifications is often misunderstood. That does not mean that grinding is prohibited on production work, just on the test (although major grinding could be weld removal and that requires engineer's approval). D1.5 WPS's must control heat input to the essential variables qualified by the PQR.
With D1.1 PQR amps can vary by +/- 10%, volts +/- 7% , travel +/- 25%, and heat input by + 10% (no limit shown for reduction in heat input)
A lot of D1.1 welding is prequalified if within the manufacturer's recommended ranges; which are pretty wide ranges.
D1.5-5.13 allows amps at +/-10%, volts +/- 7%, travel +/- 10%, and heat input is +10%/-30%.
These are for FCAW and there are other differences I didn't mention.
You could also qualify a D1.5 maximum heat input PQR, or a min/max heat input PQR.
The point is that heat input control is important with D1.5. A welder must demonstrate that he/she can weld within the essential variables and produce a sound weld. Excessive grinding and re-welding in production could adversely affect the steel.
It's late for me, I'm rambling - so I'll leave it at that. Gotta get some sleep so in the morning I can drop some Pyrodex down the barrel and find something legal to shoot.