The stability issue is one that I face in my business too - I mean I get asked the same question about long term security for my clients.
What I say is that with me they get a small outfit with low overheads, lots of personal attention and flexibility. Typical of a good SMALL project.
Having seen my husband die on the pillow next to me with no warning, I know just how uncertain life can be. (Oh I resuscitated him and that was 20 years ago, still ridiculously devoted
)
But the truth is I can't guarantee long term continuity like a big company can. I could replace anyone else in the project but it'd be very tough for them to replace me. Might do it with 3 people but that puts up the overheads.
Now if they go with a big company they get the stability. But they also get bureaucracy, distant management, switchboard paralysis listening to muzak, inefficiency through size or left hand doesn't know what right hand does. The level of enthusiasm to look after a client is rarely so high. The attention to detail on the product is not so high because responsibility is spread around.
If you want flexibility, humanity, individual attention, high standard product - go for a young small company. Work with them, help them shape the product how you want it.
If you feel stability over the years is paramount go for the big established company. But the price is distance management, you're a number not an individual, the product is unlikely to be so lovingly designed and produced. Basically what YOU want ,matters a lot less.
Your choice.