The bypass ones, that look like tree pruners but with a notch in them to hold the nail from sliding when you press closed, tend to work better IMO. Diamond makes the best quality ones.
OTOH, I think a Dremel is better still. It leaves a totally smooth edge that won't snag on panty hose (something very important to Smithcat

), it makes it harder (but not impossible) to quick a dog, and costs around $20 for a rechargeable one. If you slip on you or the dog, it doesn't really hurt unless you hold it in place for a while and press. If it just bounces off a finger you hardly notice anything but the feel of an emery board rubbing across the finger.
On the down side: they are noisy and vibrate. This can upset some dogs. It might pay to start out slowly and condition the dog to the noise and vibration before actually trimming with them.
Oh. Another down-side: toe nail dust. It's best to do this outside in a well ventilated area and while wearing clothes you don't mind getting dirty.