A standard profile hip protector will be noticeable under your clothing, but it won't feel excessively bulky or restrict your movement on the slopes. Think of it like wearing padded bike shorts—you'll see some shape, but it's not a dealbreaker for most skiers.
The key thing to consider is what you'll be wearing over it. Standard profile protectors work great under typical relaxed-fit or standard ski pants, where the extra bulk pretty much disappears. However, if you prefer slim-fitting or fitted snow pants, you'll likely see the outline of the pads.
For most recreational skiers, standard profile hits a sweet spot: you get full protection coverage without the extreme bulk of racing-style armor. Since these are the most common style of impact shorts on the market, you'll have plenty of options to choose from at reasonable prices. If you have a medical condition like osteoporosis, prioritize this level of protection over discretion—wearing something visible is always better than leaving a bulky protector at home because you're self-conscious about how it looks.