Does a larger sensor make up for lack of IS and a smaller max aperture?

Image stabilisation is relevant mostly for countering the effects of small rotations around several axes. For the overall picture, the effect of those rotations is roughly proportional to the effective focal length (but for pixel peeping, the effect grows again with the resolution). For larger sensors, one tends to have more and longer glass for the same effective focal length which stabilises by its weight. However, holding large weights when not close to the body tends to cause more of an arm musculature tremor when not using at least a monopod.

I have an old DSC-R1 camera without image stabilisation, an APS-C class sensor (crop factor 1.67 I think), only 10MP of resolution and a maximum effective focal length of 120mm, at a weight of about 1kg. At speeds of about 1/5s you have a moderate amount of success with photographs given enough practice. You can add about 1.5kg for a teleconverter giving an effective reach of 200mm. Arm shake at this weight becomes an issue.

Basically for longer focal lengths foregoing image stabilisation with handheld shots is really going to become problematic in my experience. However, in contrast to my old camera, current large sensor offerings have large usable ISO ranges so you often can use exposure times short enough that image shake is not a significant problem, and as a side benefit object movement is then not a problem either.

So if you are leaning towards a camera without image stabilisation, have a very good look at its high ISO performance and maybe also about the ability to work with external lighting (like on-camera and off-camera flash).

In looking at any competing camera models, comparing like for like is the best bet. Let's start with focal length.

• Ricoh: 28mm (35mm equivalent)
• Sony: 24mm - 70mm (35mm equivalent)

This is actually a big point as these are fixed lens cameras. You have none.nada.zero ability to zoom from the camera with the Ricoh. You can "zoom with your feet" or crop the image to "get closer" but not with the camera.

Next, let's look at the IS spec. Before getting into this, keep in mind that hand-holdable shutter speeds are usually 1/focal length. That's the "safe" range...many shooters with steady hands can go under this. So, for the Ricoh, your slowest shutter speed should be 1/28 second for you to hand hold the shots. And you're right, the larger sensor size will award better image quality in low light. To me, this effectively negates the need for IS in 99% of the situations that you'll be shooting in.

Next let's look at the apertures, f/2.8 vs f/1.8. This is a one and a third stop difference - not huge in the grand scheme of things, especially since the Ricoh will have better high ISO performance.

Recap: At 28mm, the Ricoh is more functional. The larger sensor will allow for higher ISO's at the same image quality such that any benefit of IS or 1.33 stops will be minimal, if not negated.

However...The Sony zooms. Full stop. These are not like-for-like options. If I had to shoot something at 28mm, I'd grab the Ricoh. If I wanted to shoot something at 70mm...the Sony is the only option.

I would urge you to strongly consider this factor. Even in the world of DSLR's and Mirrorless ILC's, many, many people use zooms over fixed focal length lenses due to the trade-off's.

Image stabilization is good for decreasing the shutter speed without blurrying everything into an abstract work. The same effect exposurewise can be achieved raising the ISO. However, doing this also increases noise.

Because of full frame's bigger area, the same ISO mean less electronic amplification than smallest sensors, and less amplification means less noise considering the same amplificator. However, be aware that this not always means that bigger sensors will have less noise, as camera's circuitry can be better or worse from model to model. I would recommend using Dxomark to help you decide which camera to buy. They tell you at what ISO the images start to look bad from noise.

The depth of field is not affected directly by sensor size, but from angle of view and subject distance. Bigger sensors widen the angle, making you come closer to your subject.

As money matters, usually it is cheaper to get the APS-C camera with wider aperture glass than a narrower aperture full frame setup that has equivalent performance. Also lighter.