To me, the biggest advantage to quality aftermarket springs is their longevity: app. three to six times that of factory springs. Even with consumables, replacing parts and then breaking them in (a neccessity in every case) gets old pretty fast.
Many people feel the factory D34's (and many other guns) are oversprung, meaning the mainsprings used are unneccessarily strong / long / harsh, producing an aggressive shot cycle. Some aftermarket springs / kits, especially Maccari, are appreciably smoother, and easier to cock, as well.
Tuning kit guides fit the mainspring much better than factory guides, reducing or eliminating twang, buzz and other mechanical noise. This is a bit like learning to appreciate fine coffee / whisky / whathaveyou, in that once you get used to a high quality product, the lower quality stuff, which you used to be perfectly happy with, is now just terrible. So, it's a mixed blessing. The twang / buzz doesn't make a gun inaccurate, after all.
I don't buy kits, but I do buy aftermarket parts. My 1988 T01 D34 has a cut Titan #3 mainspring now, which fit a factory rear guide perfectly, and yielded optimal velocities for a .177 cal field gun. These days, I only use Titan springs, as they are the most predictable, dependable and durable springs around. Titan does not make kits, however. Some British companies offer kits that utilize the Titans, though.
Beware that the older T01 guns often have a shorter "compression space" for the mainspring + guides than the present-day T06 guns. Some products made for the newer guns will not fit your older gun, without cutting the mainspring some. Been there.
Most people in the U.S. use either Maccari or Vortek kits in their guns. I have used Maccari springs but no kits, and I have not used Vortek kits or springs, so I'll leave recommendations on those to people who have. Both have their pro's and con's, and their fans.
Sending the gun to a reputable tuner saves you of all the potential headaches stemming from disassembly, parts fit (see above) etc., but it's not only about convenience. Most tuners have a bag o' tricks that make the gun a little bit better to shoot here and there, and the cumulative end result is an enhanced gun that a mere kit installation wouldn't yield. For an older gun, the cost may easily exceed the gun's value, but many people find it worth it, anyway.