I prefer DSL because I play games, I need the IP's, and I need control of reverse DNS. If, by stability, you mean "solid ping times," then go with DSL. Just be sure that your point of presence (POP) is nearby. After about 4 months, my ISP (Speakeasy) opened a new POP that was across the bay, which reduced the latency to my gateway from ~90 ms to ~11 ms. I'm also happy with my DL speed of 150Kb/s any time of day, but from what I hear, cable can peak far beyond that.
[edit] You should consider cost as well. In my area, "decent" DSL (like what I have) runs about $100 / mo, whereas cable runs about $40 / mo. It all depends on what you plan to do.
~bex0rs