Dyno tune is safer and kinda faster (sorta).
The problem is a dyno is... Unless you own a dyno shop and JUST dyno vettes or JUST dyno vipers or JUST dyno hondas, its very hard to get an accurate, road load simulating dyno. My srt4 was "dyno tuned" to 354whp and 505tq (thanx nitrous), but I drove off the rollers onto the street and difference in load and AFR was instantly different. I had to change the fuel on my drive home.
Dyno's are fun. I like just watching on dyno days/nights. They can really get you a long way starting with a blank sheet of paper on a new engine tune. But the fact they still can't replicate intercooler cooling, they can't perfectly replicate street load. And they are not really cheap to rent by the day, I'd say road tuning is much safer, and since your on the road you drive on, its a perfect match for the load your car is gonna see.
Besides the fact that your limited to a small amount of runs normally, and the car basically sits and heat soaks between passes ( sitting still parked ), the drag strip while datalogging prob is the best. Its safe, controlled, repeatable, and flat. Issue is.... I can get 20 rolling (non-heat soaked) pulls in a night out in the mines with no waiting, no heat soak, no cost, and consistency.
With even stock dyno's for our cars ranging from 190whp to 160whp, its pretty clear that one dyno vs the other is not constant measurement for power vs someone else. But its your looking for bragging rights, I can recommend a shop in So. Cal, lol. But numbers aside, do you want a great tune or bragging rights? Normally not the samething anyway.
If you have the power like access tuner guys do, then street tuning is a great option.