Downsides of Linoleum (in kitchen specifically)
If the tile is nice tile, I'd strongly consider keeping that. People like tiled kitchens.

Linoleum is a bit like laminate counter tops. Has a bit of a 60s/70s stigma to it. 

But also like laminate counter tops, they've gotten better and now come in a much wider range of looks.

Linoleum has the added benefit of being a 'natural/green' material, so fits into the green trend as well (which is a good trend, for the most part).

I suppose the biggest con would be that it won't wear as well (or last as long) as tile will...then again, very little will wear as well as tile.

You'll also need to decide if you want a surface that needs to be waxed regularly or has a more permanent top coat. I assume most products on the market today will have the latter, but you'll want to check into that. 

The other con is that you'll likely have to either tear out your tile, or add a new layer of plywood to the top of it. Granted, you'll probably have to do that regardless, but also something to consider.